HK1246017B - Apparatus for decoding a plurality of transform coefficients having transform coefficient levels from a data stream - Google Patents

Description

Apparatus for decoding a plurality of transform coefficients having transform coefficient levels from a data stream

This application is a divisional application of the Chinese patent application with application number 201380015410.7.

Technical Field

The present invention relates to encoding of transform coefficients, such as transform coefficients of a transform coefficient block of a picture.

Background Art

In block-based image and/or video codecs, pictures or frames are encoded in units of blocks. Transform-based codecs, on the other hand, transform blocks of pictures or frames to obtain blocks of transform coefficients. For example, pictures or frames can be coded predictively, where the prediction residuals are transform coded in units of blocks, and the resulting transform coefficients of these transform blocks are then encoded at the transform coefficient level using entropy coding.

To improve entropy coding efficiency, context is used to accurately estimate the probability of the sign at the level of the transform coefficient to be encoded. However, in recent years, the requirements imposed on picture and/or image codecs have been increasing. In addition to the luma and chroma components, codecs sometimes have to transmit depth maps, transparency values, etc. Moreover, the transform coefficient sizes are variable over an increasingly large range. Due to this diversity, codecs have an increasing number of different contexts with different functions to determine the context based on the already encoded transform coefficients.

A different possibility to achieve high compression rates with more modest complexity is to adapt the symbolization scheme as accurately as possible to the statistics of the coefficients. However, in order to perform a close adaptation to the actual statistics, various factors must also be taken into account, thereby requiring a large number of different symbolization schemes.

Therefore, there is a need to keep the complexity of transform coefficient coding low, while at the same time maintaining the possibility to achieve high coding efficiency.

Summary of the Invention

The object of the present invention is to provide such a transform coefficient coding scheme.

This object is achieved by the subject matter of the pending independent claims.

According to one aspect of the present invention, an apparatus for encoding a plurality of transform coefficients having transform coefficient levels into a stream includes: a symbolizer configured to: map the current transform coefficient to a first set of one or more symbols according to a first symbolization scheme if the transform coefficient level of the current transform coefficient is within a first level interval, and map the current transform coefficient to a maximum level of the first level interval according to a second symbolization scheme if the transform coefficient level of the current transform coefficient is within a second level interval, to a combination of a second set of symbols mapped thereto according to the first symbolization scheme and a third set of symbols according to the position of the transform coefficient level of the current transform coefficient within the second level interval, wherein the second symbolization scheme is parameterizable according to a symbolization parameter. Furthermore, the apparatus includes a context-adaptive entropy encoder configured to entropy encode a first set of one or more symbols into a data stream if a transform coefficient level of a current transform coefficient is within a first level interval, and to entropy encode a second set of one or more symbols into the data stream if a transform coefficient level of the current transform coefficient is within a second level interval, wherein the context-adaptive entropy encoder is configured to, during entropy encoding of at least one predetermined symbol of the second set of one or more symbols into the data stream, use a context based on previously encoded transform coefficients via a function parameterizable by a function parameter, wherein the function parameter is set to a first setting. Furthermore, the apparatus includes a symbolization parameter determiner configured to determine a symbolization parameter for mapping to a third set of symbols based on previously encoded transform coefficients via a function, wherein the function parameter is set to a second setting, if the transform coefficient level of the current transform coefficient is within the second level interval. An inserter is configured to insert the third set of symbols into the data stream if the transform coefficient level of the current transform coefficient is within the second level interval.

According to another aspect of the present invention, an apparatus for encoding a plurality of transform coefficients, each having a transform coefficient level, of different transform blocks into a data stream comprises: a symbolizer configured to map the transform coefficient level to a set of symbols for a current transform coefficient according to a symbolization scheme, wherein the symbolization scheme is parameterizable according to a symbolization parameter; an inserter configured to insert the set of symbols for the current transform coefficient into the data stream; and a symbolization parameter determiner configured to determine a symbolization parameter for the current transform coefficient according to previously processed transform coefficients via a function parameterizable by a function parameter, wherein the inserter, the symbolizer, and the symbolization parameter determiner are configured to process the transform coefficients of the different transform blocks in sequence, wherein the function parameter varies according to the size of the transform block of the current transform coefficient, the type of information component of the transform block of the current transform coefficient, and/or the frequency portion in which the current transform coefficient is located within the transform block.

The idea of the present invention is to use the same function for both the dependency of the context on previously coded/decoded transform coefficients and the dependency of the symbolization parameters on previously coded/decoded transform coefficients. In the case where the transform coefficients are spatially arranged in a transform block, the same function with different function parameters can even be used for different transform block sizes and/or frequency fractions of the transform block. Another variation of this idea is to use the same function for the dependency of the symbolization parameters on previously coded/decoded transform coefficients for different transform block sizes of the current transform coefficient, different information component types of the transform block of the current transform coefficient, and/or different frequency fractions within the transform block where the current transform coefficient is located.

BRIEF DESCRIPTION OF THE DRAWINGS

Detailed and advantageous aspects of the invention are the subject of the independent claims. Furthermore, preferred embodiments of the invention are described below with reference to the accompanying drawings, in which:

1 shows a schematic diagram of a transform coefficient block including transform coefficients to be encoded according to an embodiment of the present invention and illustrates that a parameterizable function is commonly used for context selection and symbolization parameter determination;

FIG2 is a schematic diagram showing the concept of symbolization of transform coefficient levels using two different schemes within two level intervals;

FIG3 is a schematic diagram showing two occurrence probability curves defined at possible transform coefficient levels for two different contexts;

FIG4 shows a block diagram of an apparatus for encoding a plurality of transform coefficients according to an embodiment;

5A and 5B are schematic diagrams showing data stream structures generated according to different embodiments;

FIG6 shows a block diagram of a picture encoder according to an embodiment;

FIG7 shows a block diagram of an apparatus for decoding a plurality of transform coefficients according to an embodiment;

FIG8 shows a block diagram of a picture decoder according to an embodiment;

FIG9 shows a schematic diagram of a transform coefficient block according to an embodiment to illustrate scanning and templates;

FIG10 shows a block diagram of an apparatus for decoding a plurality of transform coefficients according to a further embodiment;

11A and 11B are schematic diagrams showing a concept of symbolization of transform coefficient levels of two or three different schemes within a local interval of a combined entire interval range;

FIG12 shows a block diagram of an apparatus for encoding a plurality of transform coefficients according to a further embodiment; and

Figure 13 shows a schematic diagram of a transform coefficient block in order to illustrate the scanning order between the transform coefficient blocks after the sub-block order defined between the sub-blocks according to a further embodiment, and the transform coefficient block is divided into sub-blocks in order to illustrate another embodiment of the design of a parameterizable function for context selection and symbolization parameter determination.

DETAILED DESCRIPTION

For the following description, please note that the same reference numerals are used for the figures of elements that appear in more than one figure. Therefore, the description of this element for one figure should also be applicable to the description of another figure in which the element appears.

Furthermore, the description presented below preliminarily assumes that the transform coefficients to be encoded are arranged two-dimensionally to form a transform block, such as a transform block of a graph. However, the present application is not limited to image and/or video encoding. Instead, the transform coefficients to be encoded may alternatively be transform coefficients of a one-dimensional transform, such as used in audio encoding, etc.

In order to explain the problems faced by the embodiments further described below, and the ways in which the embodiments further described below overcome these problems, reference is initially made to Figures 1-3, which show examples of transform coefficients of a transform block and a general way of entropy coding, and then improved by the embodiments explained subsequently.

FIG1 exemplarily shows a block 10 of transform coefficients 12. In this embodiment, the transform coefficients are arranged two-dimensionally. In particular, the transform coefficients are exemplarily shown as being regularly arranged in columns and rows, but another two-dimensional arrangement is also possible. The transform that produces the transform coefficients 12 or transform block 10 can be a DCT or some other transform that decomposes a (transform) block of a picture, such as some other block of spatially arranged values, into components of different spatial frequencies. In the example of FIG1 , the transform coefficients 12 are arranged two-dimensionally into columns i and rows j so as to correspond to frequency pairs (f x (i), f y (j)) of frequencies f _x (i), f _y (j) measured along different spatial directions x, y, such as directions perpendicular to each other, where f _x/y (i) < f _x/y (i+1) and (i, j) are the positions of the respective components in the transform block 10.

Typically, transform coefficients 12 corresponding to lower frequencies have higher transform coefficient levels than transform coefficients corresponding to higher frequencies. Therefore, typically, many transform coefficients near the highest frequency component of the transform block 10 are quantized to zero and do not need to be encoded. Instead, a scan order 14 can be defined between the transform coefficients 12, which arranges the two-dimensionally arranged transform coefficients 12 (i, j) into a coefficient sequence in a one-dimensional manner in an order (i.e., (i, j) → k) such that the transform coefficient levels are likely to have a monotonically decreasing trend along the order, i.e., the coefficient level of coefficient k is likely to be greater than the coefficient level of coefficient k+1.

For example, a zigzag or raster scan may be defined between the transform coefficients 12. Depending on the scan, the block 10 may be scanned diagonally from, for example, the DC component transform coefficient (upper left coefficient) to the highest frequency transform coefficient (lower right coefficient) or from the highest frequency transform coefficient (lower right coefficient) to the DC component transform coefficient (upper left coefficient). Alternatively, the transform coefficients between the extreme component transform coefficients just mentioned may use row-by-row or column-by-column scanning.

As further described below, during encoding of a transform block, the position of the last non-zero transform coefficient L according to the scan order 14 may be encoded into the data stream first, and then only the transform coefficients from the DC transform coefficient along the scan path 14 to the last non-zero transform coefficient L (optionally in this direction or in the opposite direction) may be encoded.

The transform coefficients 12 have transform coefficient levels that may be signed or unsigned. For example, the transform coefficients 12 may have been obtained by the aforementioned transform and subsequently quantized to a set of possible quantization values, each quantization value being associated with a respective transform coefficient level. The quantization function used to quantize the transform coefficients, i.e., to map the transform coefficients to transform coefficient levels, may be linear or nonlinear. In other words, each transform coefficient 12 has a transform coefficient level outside the interval of possible levels. FIG2 illustrates, for example, an example in which the transform coefficient level x is limited to the level range [0, 2 ^N-1 ]. According to alternative embodiments, the interval may not have an upper limit. Furthermore, FIG2 only illustrates positive transform coefficient levels, which may also be signed. Regarding the signs of the transform coefficients 12 and their encoding, it should be noted that different possibilities exist for encoding these signs with respect to all embodiments described below, and all possibilities are intended to be within the scope of these embodiments. With respect to FIG2 , this means that the range of the transform coefficient levels may also have no lower limit.

In any case, to encode the transform coefficient levels of the transform coefficients 12, different symbolization schemes are used so as to cover different parts or intervals 16, 18 of the range interval 20. More precisely, the transform coefficient levels within the first level interval 16, except for the maximum level of the first level interval 16, can be simply symbolized onto a set of one or more symbols according to the first symbolization scheme. However, the transform coefficient levels located within the second level interval 18 are mapped onto a combination of the symbol sets of the first and second symbolization schemes. As will be noted later, the third and further intervals can thus follow the second interval.

2 , the second level interval 18 is located above the first level interval 16 but overlaps the first level interval 16 at its maximum level, which in the example of FIG2 is 2. For the transform coefficient levels within the second level interval 18, each level is mapped to a combination of a first set of symbols corresponding to the maximum level of the first level interval in accordance with a first symbolization scheme and a second set of symbols according to the position of the transform coefficient level within the second level interval in accordance with a second symbolization scheme.

In other words, the first symbolization scheme 16 maps the levels covered by the first level interval 16 onto a set of first symbol sequences. Note that the length of the symbol sequences within the set of symbol sequences of the first symbolization scheme can even be just one binary symbol in the case of a binary alphabet and in the case of a first level interval 16 covering only two transform coefficient levels, such as 0 and 1. According to an embodiment of the present application, the first symbolization scheme is a truncated unary binarization of the levels within the interval 16. In the case of a binary alphabet, the symbols can be referred to as bins.

As described in more detail below, a second symbolization scheme maps levels within a second level interval 18 to a set of second symbol sequences of different lengths, wherein the second symbolization scheme is parameterizable according to a symbolization parameter. The second symbolization scheme can map the levels within the interval 18, i.e., x minus the maximum level of the first interval, to a Rice code having a Rice parameter.

In particular, the second symbolization scheme 18 can be configured such that the symbolization parameter changes at a rate at which the length of the symbol sequence of the second scheme increases from the lower limit of the second level interval 18 to its upper limit. Obviously, increasing the length of the symbol sequence consumes more data rate in the data stream into which the transform coefficients are encoded. Generally speaking, it is preferable if the length of the symbol sequence to which a certain level is mapped is correlated with the actual probabilities of the respective levels for the transform coefficient level hypothesis currently being encoded. Naturally, this latter statement is also valid for levels within the first level interval 16 outside the second level interval 18, or for the first symbolization scheme in general.

In particular, as shown in FIG3 , transform coefficients generally exhibit certain statistical probabilities of occurring at certain transform coefficient levels. FIG3 shows a graph associating the probability of each transform coefficient level being actually assumed by the transform coefficient in question to each possible transform coefficient level x. More specifically, FIG3 shows two such correlation or probability curves, namely, for two coefficients in different contexts. That is, FIG3 assumes that the transform coefficients are determined based on their contextual distinctions, such as the transform coefficient values of neighboring transform coefficients. Depending on the context, FIG3 shows that the probability curves associating probability values with each transform coefficient level can depend on the context of the transform coefficient in question.

According to the embodiment described below, the symbols of the symbol sequence of the first symbolization scheme 16 are entropy coded in a context-adaptive manner. That is, a context is associated with the symbol, and the alphabet probability distribution associated with the selected context is used to entropy code each symbol. The symbols of the symbol sequence of the second symbolization scheme are inserted into the data stream directly or using a fixed alphabet probability distribution, such as one in which all members of the alphabet are equally likely according to the same probability distribution.

The context used to entropy encode the symbols of the first symbolization scheme must be appropriately chosen to allow the estimated letter probability distribution to be well adapted to the actual letter statistics. That is, whenever a symbol with that context is encoded/decoded, the entropy encoding scheme can be configured to update the current estimate of the context letter probability distribution, thereby approximating the actual letter statistics. This approximation is faster if the context is chosen appropriately, i.e., fine enough, but without too many different contexts to avoid symbols being too rarely associated with certain contexts.

Likewise, the symbolization parameters of the coefficients should be selected based on the coefficients of the previous encoding/decoding in order to approximate the actual letter statistics as closely as possible. Excessive diversification is not a critical issue here, since the symbolization parameters are determined directly based on the coefficients of the previous encoding/decoding, but this determination should closely correspond to the dependence of the probability curve in the second interval 18 on the coefficients of the previous encoding/decoding.

As described in more detail below, an advantage of the embodiments of encoding transform coefficients described further below is the use of common functions to achieve context adaptability and symbolization parameter determination. As previously mentioned, selecting the correct context is important for achieving high coding efficiency or compression, and the same applies to symbolization parameters. The embodiments described below allow this to be achieved by keeping the overhead of instantiating dependencies on previously encoded/decoded coefficients low. In particular, the inventors of the present application have discovered a good compromise between achieving dependencies on previously encoded/decoded coefficients on the one hand and reducing the amount of dedicated logic required to instantiate each context dependency on the other.

FIG4 shows an apparatus for encoding a plurality of transform coefficients having transform coefficient levels into a data stream according to an embodiment of the present invention. Note that in the following description, it is assumed that the symbol alphabet is a binary alphabet, but this assumption is not critical to the present invention as described above, and therefore all explanations should be interpreted as being equally illustrative for other symbol alphabets.

4 is used to encode a plurality of transform coefficients input at an input terminal 30 into a data stream 32. The apparatus includes a symbolizer 34, a context adaptive entropy encoder 36, a symbolization parameter determiner 38 and an inserter 40.

The symbolizer 34 has an input connected to the input terminal 30 and is configured to map a current transform coefficient currently input thereto into symbols in the manner described above with respect to FIG2 . That is, the symbolizer 34 is configured to map the current transform coefficient into a first set of one or more symbols according to a first symbolization scheme if the transform coefficient level x of the current transform coefficient is within the first level interval 16, and to map the current transform coefficient into a combination of a second set of symbols to which the maximum level of the first level interval 16 is mapped according to the first symbolization scheme and a third set of symbols that are dependent on the position of the transform coefficient level of the current transform coefficient within the second level interval 18 according to a second symbolization scheme if the transform coefficient level x of the current transform coefficient is within the first level interval 16 but outside the second level interval. In other words, the symbolizer 34 is configured to map the current transform coefficient into a first symbol sequence of the first symbolization scheme if the transform coefficient level of the current transform coefficient is within the first level interval 16 but outside the second level interval, and to map the current transform coefficient into a combination of the symbol sequence of the first symbolization scheme and the symbol sequence of the second symbolization scheme for the first level interval 16 if the transform coefficient level of the current transform coefficient is within the second level interval.

The symbolizer 34 has two outputs, namely an output for a symbol sequence of a first symbolization scheme and an output for a symbol sequence of a second symbolization scheme. The inserter 40 has an input for receiving a symbol sequence 42 of the second symbolization scheme, and the context adaptive entropy encoder 36 has an input for receiving a symbol sequence 44 of the first symbolization scheme. Furthermore, the symbolizer 34 has a parameter input for receiving a symbolization parameter 46 from the output of the symbolization parameter determiner 38.

The context adaptive entropy encoder 36 is configured to entropy encode the symbols of the first symbol sequence 44 into the data stream 32. The inserter 40 is configured to insert the symbol sequence 42 into the data stream 32.

In general, the entropy encoder 36 and the inserter 40 scan the transform coefficients sequentially. Obviously, the inserter 40 operates only on transform coefficients whose transform coefficient levels are within the second level interval 18. However, as described in more detail below, there are different possibilities for defining the order between the operations of the entropy encoder 36 and the inserter 40. According to a first embodiment, the encoding device of FIG4 is configured to scan the transform coefficients in a single scan, so that the inserter 40 inserts the symbol sequence 42 of the transform coefficients into the data stream 32 after the entropy encoder has encoded a first symbol sequence 44 associated with the same transform coefficient into the data stream 32 and before the entropy encoder has entropy encoded a symbol sequence 44 associated with the next transform coefficient in a line into the data stream 32.

According to an alternative embodiment, the apparatus uses two scans, wherein in a first scan the context adaptive entropy encoder 36 encodes the sequence of symbols 44 into the data stream 32 for each transform coefficient in turn, and the inserter 40 then inserts the sequence of symbols 42 for transform coefficients whose transform coefficient levels are within the second level interval 18. Even more complex schemes are possible, for example, whereby the context adaptive entropy encoder 36 uses several scans in order to encode individual symbols of the first sequence of symbols 44 into the data stream 32, such as the first symbol or bin of the first scan following the second symbol or bin of the sequence 44 in the second scan.

As already indicated above, the context adaptive entropy encoder 36 is configured to entropy encode at least one predetermined symbol of the symbol sequence 44 into the data stream 32 in a context adaptive manner. For example, the context adaptability is applied to all symbols of the symbol sequence 44. Alternatively, the context adaptive entropy encoder 36 may limit the context adaptability to the symbols at the first position and the symbol sequence of the first symbolization scheme, or the first and second, or the first to third positions, etc.

As described above, for context adaptability, encoder 36 manages contexts by storing and updating an estimate of the probability distribution of letters for each context. Whenever a symbol of a context is encoded, the currently stored estimate of the probability distribution of letters is updated with the actual value of that symbol, thereby approximating the actual letter statistics of the symbols of that context.

Likewise, the symbolization parameter determiner 38 is configured to determine the symbolization parameters 46 of the second symbolization scheme and its symbol sequence 42 as a function of previously encoded transform coefficients.

More specifically, the context adaptive entropy encoder 36 is configured to use or select a context for a current transform coefficient based on previously encoded transform coefficients via a function parameterizable by a function parameter, wherein the function parameter is set to a first setting, while the symbol parameter determiner 38 is configured to determine the symbolization parameter based on previously encoded transform coefficients via the same function, wherein the function parameter is set to a second setting. The settings may be different, but since the symbolization parameter determiner 38 and the context adaptive entropy encoder 36 use the same function, the logic overhead may be reduced. The function parameter may only differ between context selection by the entropy encoder 36 on the one hand and symbolization parameter determination by the symbolization parameter determiner 38 on the other hand.

With respect to dependencies on previously encoded transform coefficients, it should be noted that such dependencies are limited to the extent that these previously encoded transform coefficients have already been encoded into the data stream 32. For example, imagine that this previously encoded transform coefficient lies within the first level interval 18, but its symbol sequence 42 has not yet been inserted into the data stream. In this case, the symbolization parameter determiner 38 and the context-adaptive entropy encoder 36 only know from the first symbol sequence 44 of this previously encoded transform coefficient that it lies within the second level interval 18. In this case, the maximum level of the first level interval 16 can serve as a representative of this previously encoded transform coefficient. In this context, dependencies on previously encoded transform coefficients should be broadly understood to include dependencies on information about other transform coefficients previously encoded/inserted into the data stream 32. Furthermore, transform coefficients outside the last non-zero coefficient L can be inferred to be zero.

4 , the outputs of the entropy coder 36 and the inserter 40 are shown connected to a common output 48 of the apparatus via a switch 50, the same connectivity existing between the inputs of the symbolization parameter determiner 38 and the previously inserted/encoded information of the context adaptive entropy coder 36 on the one hand and the outputs of the entropy coder 36 and the inserter 40 on the other hand. The switch 50 connects the output 48 to any one of the outputs of the entropy coder 36 and the inserter 40 for the various possibilities of using one, two or more scans for encoding the transform coefficients, in the order mentioned above.

To more specifically explain the shared use of parameterizable functions for the context-adaptive entropy encoder 36 and the symbolization parameter determiner 38, reference is made to FIG. A function commonly used by the entropy encoder 36 and the symbolization parameter determiner 38 is indicated at 52 in FIG. 1 , namely, g(f(x)). This function is applied to a set of previously encoded transform coefficients, which, as explained above, can be defined as containing previously encoded coefficients having a certain spatial relationship relative to the current coefficient. Specific embodiments of this function will be described in more detail below. In general, f is a function that combines a set of previously encoded coefficient levels into a scalar, while g is a function that checks the interval within which the scalar lies. In other words, the function g(f(x)) is applied to a set x of previously encoded transform coefficients. In FIG. 1 , the transform coefficient 12 represented by a small cross, e.g., the current transform coefficient, and the shaded transform coefficient 12 indicate the set x of transform coefficients to which the function 52 is applied to obtain the symbolization parameters 46 and the entropy context index 54 that indexes the context of the current transform coefficient x. As shown in FIG1 , a local template defining the relative spatial arrangement around the current transform coefficient can be used to determine a set x of relevant previously coded transform coefficients that are outside the range of all previously coded transform coefficients. As can be seen in FIG1 , the template 56 can include the transform coefficients immediately below and to the right of the current transform coefficient. By selecting the template in this way, the symbol sequences 42 and 44 of the transform coefficients on one diagonal of the scan 410 can be encoded in parallel because no transform coefficient on the diagonal falls within the template 56 of another transform coefficient on the same diagonal. Naturally, similar templates can be found for row-by-row and column-by-column scanning.

To provide more specific examples of commonly used functions g(f(x)) and corresponding function parameters, these examples are provided below using various formulas. In particular, the apparatus of FIG4 can be configured so that the function 52 defining the relationship between the set x of previously encoded transform coefficients on the one hand and the context index number 54 indexing the context and symbolization parameters 46 on the other hand can be:

g(f(x)), where

in

and

in

t and, optionally _{, wi} form the function parameters,

x＝{x ₁ ,...,x _{d }} , where x i∈{1...d} represents the previously decoded transform coefficient i,

w _i are weight values, each of which may be equal to one or not, and

h is a constant or a function of _xi .

Therefore, g(f(x)) lies within [0, _df ]. If g(f(x)) is used to define a context index offset number ctx _offset that is summed with at least one base context index offset number ctx _base , the resulting context index ctx = ctx _base + ctx _offset has a value range of [ctx _base ; ctx _base + _df ]. Whenever a different set of contexts is proposed for entropy coding a symbol of the symbol sequence 44, ctx _base is selected in a different manner so that [ctx _{base, 1} ; ctx _base + _df ] does not overlap with [ctx _{base, 2} ; ctx _base + _df ]. For example, the following is true:

Transform coefficients belonging to transform blocks of different sizes;

Transform coefficients of transform blocks belonging to different information component types such as depth, luma, chroma, etc.

• Transform coefficients of different frequency parts belonging to the same transform block.

As mentioned above, the symbolization parameter may be the Rice parameter k. That is, the (absolute) level in interval 16, i.e., X, where X+M=x (where M is the maximum level in interval 16 and x is the (absolute) transform coefficient level), may be mapped onto a bin string with a prefix and a suffix, the prefix being a unary code of and the suffix being a binary code of the remainder of X·2 ^-k .

d _f can also form part of a function's arguments. d can also form part of a function's arguments.

For example, the difference in function parameters between context selection and symbolic parameter determination requires only a difference in either t, _df (if forming part of the function parameters), or d (if forming part of the function parameters).

As described above, the index i may index the transform coefficient 12 within the template 56. In the case where the respective template position is outside the transform block, x _i may be set to zero. Further, the context adaptive entropy encoder 36 may be configured such that the dependency of the context from the previously encoded transform coefficient is via a function such that x _i is equal to the transform coefficient level of the previously encoded transform coefficient i if the transform coefficient level is within the first level interval 16 and equal to the maximum level of the first level interval 16 if the transform coefficient level of the previously encoded transform coefficient i is within the second level interval 18, or such that x _i is equal to the transform coefficient level of the previously encoded transform coefficient i, regardless of whether the transform coefficient level of the previously encoded transform coefficient i is within the first or second level interval.

As far as the symbolization parameter determiner is concerned, it can also be configured so that, in the process of determining the symbolization parameter, x _i is equal to the transform coefficient level of the previously encoded transform coefficient i, regardless of whether the transform coefficient level of the previously encoded transform coefficient i is within the first or second level interval.

The device can also be configured to be suitable for any situation.

The apparatus may also be configured such that h = | _xi | - t.

In a further embodiment, the apparatus may be configured to spatially determine previously coded transform coefficients in dependence on the relative spatial arrangement of said transform coefficients with respect to the current transform coefficient, ie based on a template around the position of the current transform coefficient.

The device can also be configured to determine the position of the last non-zero transform coefficient L among the transform coefficients of the transform coefficient block 10 along a predetermined scanning order 14, and insert information about the position into the data stream 32, wherein the multiple transform coefficients include the transform coefficients from the last non-zero transform coefficient L to the beginning of the predetermined scanning order, i.e., the DC component transform coefficient.

In a further embodiment, the symbolizer 34 may be configured to use a modified first symbolization scheme for symbolizing the last transform coefficient L. According to the modified first symbolization scheme, only non-zero transform coefficient levels within the first level interval 16 may be mapped, while it is presumed that the zero level should not be applied to the last transform coefficient L. For example, a truncated unary binarized first bin may be suppressed for the coefficient L.

The context adaptive entropy encoder may be configured to use a separate set of contexts for entropy encoding the first set of one or more symbols of the last non-zero transform coefficients that is independent of the contexts for entropy encoding the first set of one or more symbols other than the last non-zero transform coefficients.

The context adaptive entropy encoder may traverse the plurality of transform coefficients in a reverse scanning order from the last non-zero transform coefficient of the transform coefficient block to the DC transform coefficient. The same may or may not apply to the second symbol sequence 42.

The apparatus may also be configured to encode a plurality of transform coefficients into a data stream 32 in two scans, wherein the context adaptive entropy encoder 36 may be configured to entropy encode a sequence of symbols 44 of transform coefficients into the data stream 32 in an order corresponding to the first scan of the transform coefficients, wherein the inserter 40 is configured to subsequently insert the sequence of symbols 42 of transform coefficients having transform coefficient levels within the second level interval 18 into the data stream 32 in an order corresponding to the occurrence of transform coefficients having transform coefficient levels within the second level interval 18 within the second scan of the transform coefficients. An example of the resulting data stream 32 is shown in FIG5A : it may include, optionally in information 57 about the position of L, the sequence of symbols 42 in entropy coded form (at least some in context adaptive entropy coded form) and further followed by the sequence of symbols 44 inserted directly or using, for example, a bypass mode (equal probability alphabet).

In a further embodiment, the apparatus may be configured to sequentially encode a plurality of transform coefficients into a data stream 32 in one scan, wherein the context adaptive entropy encoder 36 and the inserter 40 are configured to, for each transform coefficient in the scan order of one scan, immediately after the context adaptive entropy encoder entropy encodes the symbol sequence 44 into the data stream 32, insert the symbol sequence 42 of each transform coefficient having a transform coefficient level within the second level interval 18 into the data stream 32, while forming a combination onto which the same transform coefficient is mapped, so that the symbol sequence 42 is inserted into the data stream 32 between the symbol sequences 44 of the transform coefficients. The result is shown in FIG5B.

The inserter 40 may be configured to insert the symbol sequence 42 into the data stream directly or using entropy coding using a fixed probability distribution. The first symbolization scheme may be a truncated unary binarization scheme. The second symbolization scheme may be such that the symbol sequence 42 is a Rice code.

As mentioned above, the embodiment of FIG. 4 can be implemented within an image/video encoder. An example of such an image/video encoder or picture encoder is shown in FIG. The picture encoder is generally designated by reference numeral 60 and includes, for example, a device 62 corresponding to the device shown in FIG. 4 . Encoder 60 is configured to, during the encoding of a picture 64, transform a block 66 of picture 64 into a transform coefficient block 10, which is then processed by device 62 to encode its plurality of transform coefficients per transform block 10. Specifically, device 62 processes transform block 10 on a transform block-by-transform block basis. In doing so, device 62 can apply function 52 to blocks 10 of varying sizes. For example, a hierarchical multi-tree subdivision can be used to decompose picture 64 or a tree root block thereof into blocks 66 of varying sizes. The transform blocks 10 resulting from applying the transform to these blocks 66 thus have varying sizes, and while function 52 can be optimized for different block sizes by using different function parameters, the overall overhead of providing different dependencies between symbolization parameters, on the one hand, and context indices, on the other, remains low.

FIG7 illustrates an apparatus for decoding a plurality of transform coefficients having transform coefficient levels from a data stream 32, which is adapted from the apparatus described above with respect to FIG4. Specifically, the apparatus of FIG7 includes a context-adaptive entropy decoder 80, a desymbolizer 82, an extractor 84, and a symbolization parameter determiner 86. The context-adaptive entropy decoder 80 is configured to entropy decode a first set of one or more symbols, i.e., a symbol sequence 44, from the data stream 32 for a current transform coefficient. The desymbolizer 82 is configured to map the first set of one or more symbols, i.e., the symbol sequence 44, to transform coefficient levels within a first level interval 16 according to a first symbolization scheme. More specifically, the context-adaptive entropy decoder 80 and the desymbolizer 82 operate in an interactive manner. The desymbolizer 82 notifies the context-adaptive entropy decoder 80 of the completion of a valid symbol sequence for the first symbolization scheme via a signal 88, which is obtained by sequentially decoding the symbols from the data stream 32 through the decoder 80.

Extractor 84 is configured to extract a second set of symbols, i.e., symbol sequence 42, from data stream 32 if the transform coefficient level to which the first set of one or more symbols, i.e., symbol sequence 44, is mapped according to the first symbolization scheme is the maximum level for level interval 16. Furthermore, desymbolizer 82 and extractor 84 may operate in coordination. That is, upon completion of a valid symbol sequence for the second symbolization scheme, desymbolizer 82 may notify extractor 84 via signal 90, so that extractor 84 may complete extraction of symbol sequence 42.

The desymbolizer 82 is configured to map the second set of symbols, ie the symbol sequence 42 , to positions within the second level interval 18 according to a second symbolization scheme which, as already mentioned above, is parameterizable according to the symbolization parameter 46 .

The context-adaptive entropy decoder 80 is configured to use, via a function, a context based on previously decoded transform coefficients during entropy decoding of at least one predetermined symbol of the first symbol sequence 44. The symbolization parameter determiner 86 is configured to determine, via a function 52, a symbolization parameter 46 based on the previously decoded transform coefficients if the transform coefficient level to which the first symbol sequence 44 is mapped according to the first symbolization scheme is the maximum level of the first level interval 16. To this end, the inputs of the entropy decoder 80 and the symbolization parameter determiner 86 are connected via a switch 92 to the output of the desymbolizer 82, where the desymbolizer 82 outputs the value x _i of the transform coefficient.

As described above, for context adaptability, decoder 80 manages contexts by storing and updating an estimate of the probability distribution of letters for each context. Whenever a symbol of a context is decoded, the actual/decoded value of that symbol is used to update the currently stored estimate of the probability distribution of letters, thereby approximating the actual letter statistics of the symbols of that context.

Likewise, the symbolization parameter determiner 86 is configured to determine the symbolization parameters 46 and the symbol sequence 42 of the second symbolization scheme as a function of previously decoded transform coefficients.

Generally speaking, all possible modifications and further details described above for encoding are also transferable to the apparatus for decoding of FIG. 7 .

FIG8 shows a supplement to FIG6 . That is, the apparatus of FIG7 can be implemented within a picture decoder 100. The picture decoder 100 of FIG7 includes an apparatus according to FIG7 , namely apparatus 102. The picture decoder 100 is configured to, during decoding or reconstruction of the picture 104, retransform a block 106 of the picture 104 from a transform coefficient block 10. The apparatus 102 decodes a plurality of transform coefficients from a data stream 32, which is then input to the picture decoder 100. In particular, the apparatus 102 processes the transform block 10 block by block and, as already indicated above, can apply the function 52 to blocks 106 of different sizes.

It should be noted that the picture encoder and decoder 60 and 100, respectively, can be configured to use predictive coding, wherein the transform/retransform is applied to the prediction residual. Furthermore, the data stream 32 can have subdivision information encoded therein, which indicates to the picture decoder 100 the subdivision into blocks that are respectively transformed.

In other words, the above-described embodiment will be described again below, with further details provided on specific aspects that can be transferred to the above-described embodiment, respectively. That is, the above-described embodiment relates to a specific way of modeling context for encoding syntax elements related to transform coefficients, such as in block-based image and video encoders, and aspects thereof are further described and highlighted below.

Embodiments may relate to the field of digital signal processing, and in particular, to methods and apparatus for image and video decoders and encoders. In particular, according to the described embodiments, encoding of transform coefficients and their associated syntax elements in block-based image and video codecs may be performed. Within this scope, some embodiments represent improved context modeling for encoding syntax elements related to transform coefficients, utilizing an entropy encoder employing probabilistic modeling. Furthermore, a derivation of Rice parameters for adaptive binarization of residual absolute transform coefficients may be performed for the symbolization parameters as described above. Benefits of the embodiments are unification, simplification, parallel processing friendliness and moderate memory usage of the context memory compared to simple context modeling.

In other words, embodiments of the present invention may disclose novel methods for context model selection for syntax elements associated with encoding transform coefficients in block-based image and video encoders. Further, derivation rules for symbolization parameters (such as Rice parameters) that control the binarization of residual values of absolute transform coefficients are described. Essentially, the above embodiments use a simple and common set of rules to perform context model selection for all or part of the syntax elements associated with encoding transform coefficients.

The first symbolization scheme mentioned above can be a truncated unary binarization. If so, coeff_significant_flag, coeff_abs_greater_1 and coeff_abs_greater_2 can be referred to as binary syntax elements or syntax, which form the first, second and third bins generated by the truncated unary binarization of the transform coefficients. As mentioned above, the truncated unary binarization can only represent a prefix, which is completed by a suffix (which itself is a Rice code) when the level of the transform coefficient falls within the second level interval 18. Another suffix can belong to an exponential Golomb code (Exp-Golombcode), such as order 0, thereby forming another level interval (not shown in Figure 2) following the first and second intervals 16 and 18 in Figure 2.

As described above, the derivation of Rice parameters for adaptive binarization of the residual absolute transform coefficients can be performed based on the same set of rules 52 as used for context model selection.

Regarding the scanning order, it should be noted that this can also be varied compared to the above description. Furthermore, different block sizes and shapes can be supported by the apparatus of Figures 4 and 6 using the same set of rules, i.e., the same function 52. Thus, a unified and simplified approach to context model selection for syntax elements associated with coded transform coefficients can be achieved, with a harmonious combination of context model selection and symbolization parameter derivation. Thus, context model selection and symbolization parameter derivation can utilize the same logic, which can be hardwired, programmed hardware, or software subroutines.

In order to achieve a common and simple solution for context model selection and derivation of symbolic parameters (such as Rice parameters), the already coded transform coefficients of the block or shape can be evaluated as described above. To evaluate the already coded transform coefficients, the separation in the process of encoding coeff_significant_flag (which is the first bin resulting from binarization) (which can be called a coded significance map) and the residual absolute value of the transform coefficient level is performed using a common function 52.

The flag information can be encoded in an interleaved fashion, i.e., by encoding the flag directly after encoding the absolute transform coefficients. Thus, the entire transform coefficients can be encoded in a single scan pass. Alternatively, the flag information can be encoded in a separate scan pass, as long as the evaluation value f(x) depends only on the absolute level information.

As described above, the transform coefficients can be encoded in a single pass or in multiple passes. This can be enabled or described by a cutoff set c, whose coefficients c _i represent the number of symbols for the transform coefficients (first and second) processed in scan i. In the case of an empty cutoff set, a single scan can be used. In order to obtain improved results for context model selection and symbolization parameter derivation, the first cutoff parameter c ₀ of the cutoff set c should be greater than 1.

Note that the cutoff set c can be chosen to be c = {c ₀ ; c ₁ }, where c ₀ = 1 and c ₁ = 3 and |c| = 2, where c ₀ represents the number of bins/symbols of the first binarization contained in the first scan, c ₁ = 3 represents the symbol positions within the first binarization, and the symbol positions covered by the symbols of the first binarization are the symbol positions of the second scan. Another example is given when the scheme encodes the first bin resulting from the binarization of the entire block or shape in the first pass, followed by encoding the second bin of the entire block or shape in the second pass, where c ₀ equals 1, c ₁ equals 2, and so on.

A local template 56 for encoding coeff_significant_flag, i.e., the first bin generated by the binarization process, can be designed as shown in FIG1 or as shown in FIG9 . For unification and simplification, the local template 56 can be used for all block sizes and shapes. Instead of evaluating only the number of neighbors of the transform coefficient that is not equal to zero, the entire transform coefficient is input to the function 52 in the form of x _i . Note that the local template 56 can be fixed, i.e., independent of the position or scan index of the current transform coefficient and independent of the previously encoded transform coefficients, or adaptive, i.e., dependent on the position or scan index of the current transform coefficient and/or the previously encoded transform coefficients, and the size can be fixed or adaptive. Furthermore, when the template size and shape are adjusted to allow coverage of all scan positions of the block or shape, all already encoded transform coefficients or all already encoded transform coefficients up to a certain limit are used for the evaluation process.

As an example, FIG9 shows another example of a local template 56 for an 8x8 transform block 10 that can be used for a diagonal scan 14. L represents the least significant scan position and the scan position is labeled x, where x represents the current scan position. Note that for other scan orders, the local template can be modified to conform to the scan order 14. For example, in the case of a forward diagonal scan, the local template 56 can be flipped diagonally.

The context model selection and symbolization parameter derivation can be based on different evaluation values f(x) generated by the already coded neighbors x _i . This evaluation is performed for all scan positions with already coded neighbors covered by the local template 56. The local template 56 can have a variable or fixed size and can depend on the scan order. However, the template shape and size are only adaptive to the scan order, so the derived value f(x) is independent of the scan order 140 and the shape and size of the template 56. Note that the size and shape of the template 56 are set so that all scan positions of the block 10 are covered for each scan position, thereby enabling the use of all already coded transform coefficients of the current block or shape.

As mentioned before, the evaluation value f(x) is used for selecting the context model index and for deriving the symbolization parameters. In general, a general set of mapping functions maps the resulting evaluation value f(x) onto a context model index and specific symbolization parameters. In addition to this, additional information as the current spatial position or the least significant scan position L of the current transform coefficient inside the transform block or shape 10 can be used to select the context model relevant for encoding the transform coefficient and can be used to derive the symbolization parameters. Note that the information or the last information resulting from the evaluation and the spatial position can be combined, so there may be a specific weighting. After the evaluation and derivation process, all parameters (context model index, symbolization parameters) can be used to encode the entire transform coefficient level or the transform coefficients up to a certain limit.

As an example configuration of the presented invention, the cutoff setting size is null. This means that each transform coefficient is completely transmitted before the next transform coefficient is processed in scan order.

The evaluation value f(x) can be generated by the evaluation of the already encoded neighbors x _i covered by the local template 56. A specific mapping function _ft (x) maps the input vector to an evaluation value for selecting a context model and Rice parameters. The input vector x can be composed of the transform coefficient values _xi of the neighbors covered by the local template 56 and according to the interleaving scheme. For example, if the cutoff set c is empty and the flag is encoded in a single pass scan, the vector x consists only of the absolute transform coefficients _xi . In general, the values of the input vector x can be signed or unsigned. The mapping function can be established as follows using an input vector x of size d (assuming t is input as a constant).

More specifically, the mapping function _ft (x) can be defined using an input vector x of size d as follows (assuming t is input as a constant).

That is, g _t ( _xi ) can be (| _xi |-t). In the latter formula, the function δ is defined as follows (assuming t is input as a constant).

Another evaluation value is the number of adjacent absolute transform coefficient levels that are greater or less than a certain value t, defined as follows.

Note that for both evaluation values, additional weighting factors are possible to control the importance of specific neighbors. For example, the weighting factor _wi can be higher for neighbors with shorter spatial distances than for neighbors with greater spatial distances. Furthermore, when all _wi are set to 1, weighting is ignored.

As an example configuration of the invention presented, f ₀ , f ₁ , f ₂ and f ₃ are evaluation values, where {0, 1, 2, 3} and the respective t of δ( _xi ) are defined as in (1). For this example, f ₀ is used to derive the context index for the first bin, f ₁ is used for the second bin, f ₂ is used for the third bin, and f ₃ is used for the Ricean parameters. In another example configuration, f ₀ is used for context model selection for the first bin, while f ₁ is used for context model selection for the second bin, the third bin, and the Ricean parameters. Here, the Ricean parameters serve as a proxy for the other symbolization parameters as well.

The same logic is used for context model selection for all syntax elements or bin indices and symbolic parameters during entropy coding, using the evaluation value f(x). In general, a particular evaluation value f(x) is mapped to a context model index or symbolic parameter using another mapping function g(x,n). The specific mapping function is defined as follows, where d is the size of the input vector n.

For this mapping, the function δ(x,n) can be defined as follows.

The size d of the input vector n and the values of the vector n may be variable and depend on syntax elements or bin indices.Furthermore, the spatial position inside the transform block or shape may be used to add or subtract (or shift) the selected context model index.

When encoding/decoding transform coefficients, in the process of scanning them, the first scanning position can be the last scanning position L when the scanning direction of Figure 1 pointing from DC to the highest frequency is applied. That is, at least the first scan in the scan for traversing the coefficients for encoding/decoding them can be directed from coefficient L to DC. For this scanning position L, the first bin index can be ignored because the last information already indicates that the scanning position consists of transform coefficients that are not equal to zero. For this scanning position, a separate context model index can be used to encode the second bin and the third bin generated by the binarization of the transform coefficients.

As an example configuration of the present invention, the resulting evaluation value f ₀ is used as input together with the input vector n = {1, 2, 3, 4, 5}, and the resulting value is the context model index of the first bin. Note that when the evaluation value is equal to zero, the context index is zero. The same scheme uses the evaluation value f ₁ and the input vector n = {1, 2, 3, 4} and the resulting values are the context model indices of the binarized second and third bins. For the Rice parameters, f ₃ and n = {0, 5, 19} are used. Note that the maximum Rice parameter is 3, so the maximum Rice parameter is not changed compared to the state-of-the-art technology by the presented invention. Optionally, f ₁ can be used to derive Rice parameters. For this configuration, the input vector should be modified to n = {3, 9, 21}. Note that the underlying set of rules is the same for all syntax elements or bin indices and Rice parameters, only the parameter or threshold set (input vector n) is different. Further, depending on the diagonal of the current scan position, the context model index can be modified, as described above, by adding or subtracting specific amounts. An equivalent description of this is to select another non-overlapping context model set. In the example implementation, if the current scan position is on the first two diagonals, the resulting context model index for the first bin is shifted by 2*|ctx0|. If the current scan position is on the third and fourth diagonals, the context model index for the first bin is shifted by |ctx0|, where |ctx0| is the maximum number of context models generated by the derivation basis for the evaluation value of generating a non-overlapping context model set. This concept is only used for the luma plane for example implementation, while no further offset is added in the case of chroma to avoid context dilution (i.e., not enough bins are encoded using the adaptive context model and the statistics cannot be tracked by the context model). The same technique can be applied to the context model indexes for the second and third bins. Here, in the example configuration of the invention presented, the threshold diagonals are 3 and 10. Again, this technique is only applied to luma signals. Note that this technique can also be extended to chroma signals. Further, note that additional index offsets based on diagonals can be established as follows.

cix _offset = d _j * idx _inc

In this formula, _dj represents the weight of the diagonal for the current scan position, and _idxinc represents the step size. Furthermore, note that the offset indices can be reversed for practical implementations. For the example implementation presented, the inversion can be done by setting the extra indices to zero, shifting the third and fourth diagonals by |ctx0| if the current scan position is on the first and second diagonals, and by 2*|ctx0| otherwise. Using the given formula, the same behavior for the example configuration is achieved when _d0 and _d1 are set to 2, _d3 and _d4 are set to 1, and all remaining diagonal factors are set to 0.

Even if the context model index is the same for different block sizes or plane types (e.g., luma and chroma), the base context model index can be different, resulting in a different set of context models. For example, the same base index can be used for block sizes larger than 8x8 in luma, while the base index can be different for 4x4 and 8x8 in luma. To obtain a meaningful number of context models, the base index can however be grouped in different ways.

As an example configuration, the context models for the 4x4 block and the residual block can be different for luma, while the same base index can be used for chroma signals. In another example, the same base index can be used for both luma and chroma signals, while the context models for luma and chroma are different. In addition, the context models for the second and third bins can be grouped, resulting in less context memory. If the context model index derivation for the second and third bins is the same, the same context model can be used to transmit the second and third bins. By properly combining base index grouping and weighting, a meaningful number of context models can be achieved, saving context memory.

In a preferred embodiment of the present invention, the cutoff set c is empty. That is, only one scan is used. For this preferred embodiment, the flag information can be interleaved using the same scan or can be encoded in a separate scan. In another preferred embodiment, the set size c is equal to 1 and c ₀ , and the first and only value of the cutoff set c is equal to 3. This corresponds to the example shown above by using two scans. In this preferred embodiment, context model selection can be performed for all three bins produced by the truncated unary binarization, while symbolization parameter derivation such as Rice parameter selection can be performed using the same function 52.

In a preferred embodiment, the size of the local template is 5. The size of the local template can be 4. For this preferred embodiment, compared to Figure 8, neighbors with a spatial distance of 2 in the vertical direction can be removed. In another preferred embodiment, the template size is adaptive and adjusted to the scanning order. For this preferred embodiment, neighbors previously encoded in the processing step are not included in the template, only as in the cases of Figures 1 and 8. By doing so, dependencies or delays are shortened, resulting in a higher processing order. In another preferred embodiment, the template size and shape are adjusted to be large enough (for example, the same block or shape size of the current block or shape). In another preferred embodiment, two local templates can be used and they can be combined by weighting factors. For this preferred embodiment, the local templates can be different in size and shape.

In a preferred embodiment, f ₀ can be used to select the context model index for the first bin and f ₁ for the second bin, the third bin and the Rice parameter. In this preferred embodiment, the input vector n = {0, 1, 2, 3, 4, 5} generates 6 context models. The input vector n for the second and third bin indices can be the same and n = {0, 1, 2, 3, 4}, while the input vector n for the Rice parameter can be n = {3, 9, 21}. In addition, in a preferred embodiment, the aforementioned frequency portion of the transform block in which a separate context set can be used can be formed by a non-intersecting set of diagonals (or lines) scanned diagonally (raster). For example, different numbers of context base offsets can exist for the first and second diagonals, and can exist for the second and third diagonals and the fourth and fifth diagonals when viewed from the DC component, so that the context selection of the coefficients in these diagonals occurs within a non-intersecting set of contexts. Note that the first diagonal is 1. For the second and third bin indices, the diagonals in the range [0,2] have a weighting factor of 2, and the diagonals in the range [3,9] have a weighting factor of 1. These additional offsets are used in the case of the luma signal, while the weighting factors for the chroma are all equal to zero. Also for this preferred embodiment, the context models for the second and third bin indices for the first scan position (which is the least significant scan position) are separated from the remaining context models. This means that the evaluation process cannot select this separate context model.

In a preferred embodiment, a 4x4 luma block or shape uses a single set of contexts for the first bin, while the context models for the remaining block sizes or shapes are the same. In this preferred embodiment, there is no separation between the block sizes or shapes used for the chroma signals. In another preferred embodiment of the present invention, there is no separation between the block sizes or shapes, resulting in the same base index or set of context models for both block sizes and shapes. Note that for these two preferred embodiments, different sets of context models are used for luma and chroma signals.

In the following, an embodiment using modified Rice parameter binarization according to the above embodiment is shown, but without context adaptive entropy coding. According to this optional coding scheme, only the Rice binarization scheme is used (optionally adding an exponential Golomb suffix). Therefore, no adaptive context model is needed to encode the transform coefficients. For this optional coding scheme, the Rice parameter derivation uses the same rules for the above embodiment.

In other words, in order to reduce complexity and context memory and improve the latency of the encoding pipeline, an optional encoding scheme based on the same set of rules or logic is described. For the optional encoding scheme, context model selection is prohibited for the first three bins produced by the binarization, and the first three bins produced by the truncated unary binarization, i.e., the first symbolization scheme, can be encoded with a fixed same probability (i.e., with a probability of 0.5). Optionally, the truncated unary binarization scheme is omitted and the interval limits of the binarization scheme are adjusted. In this use, the left limit of the Rice interval, i.e., interval 18, is 0 instead of 3 (interval 16 disappears). The right/upper limit used for this purpose can be left unchanged or can be subtracted by 3. The derived Rice parameters can be modified based on the evaluation value and based on the input vector n.

Thus, according to the modified example just outlined, an apparatus for decoding a plurality of transform coefficients, each having a transform coefficient level, of different transform blocks from a data stream 32 may be constructed and operated as shown and described with respect to FIG. 10 .

The apparatus of Figure 10 comprises an extractor 120 configured to extract a set of symbols or a sequence of symbols 122 from the data stream 32 of the current transform coefficient. This extraction is performed as described above with respect to the extractor 84 of Figure 7 .

The de-symbolizer 124 is configured to map the set of symbols 122 onto the transform coefficient levels of the current transform coefficient according to a symbolization scheme that is parameterizable according to a symbolization parameter. This mapping may only use a parameterizable symbolization scheme, such as Rice binarization, or may only use the parameterizable symbolization scheme as a prefix or suffix to the overall symbolization of the current transform coefficient. With respect to FIG. 2 , for example, the parameterizable symbolization scheme, i.e., the second symbolization scheme, forms a suffix relative to the symbol sequence of the first symbolization scheme.

For further examples, refer to Figures 11A and 11B. According to Figure 11A, the range of transform coefficients 20 is subdivided into three ranges 16, 18, and 126, which together cover the range 20 and overlap at the maximum level of each lower range. If the coefficient level x is within the highest range 126, the overall symbolization is a combination of the symbol sequence 44 of the first symbolization scheme 128 symbolizing the levels within range 16, the symbol sequence forming a prefix following the first suffix, i.e., the second symbolization scheme 130 symbolizing the levels within range 18, and the symbol sequence 42 further following the second suffix, i.e., the third symbolization scheme 134 symbolizing the levels within range 126. The latter can be an Exponential Golomb code, such as order 0. If the coefficient level x is within the middle range 18 (but not within range 126), the overall symbolization is simply a combination of the prefix 44 following the first suffix 42. If the coefficient level x is within the lowest range 16 (but not within range 18), the overall symbolization consists solely of the prefix 44. The overall symbolization is composed so that it is prefix-free. Without the third symbolization, the symbolization according to FIG. 11A may correspond to the symbolization of FIG. 2 . The third symbolization scheme 134 may be a Columbine binarization. The second symbolization scheme 130 may form a parameterizable symbolization scheme, but it may also be the first 128.

Optional overall symbolization is shown in FIG1 . Here, only two symbolization schemes are combined. Compared to FIG11A , the first symbolization scheme remains. Depending on x within interval 136 of scheme 134 or interval 138 (outside interval 136) of scheme 130, the symbolization of x includes prefix 140 and suffix 142, or only prefix 140.

10 further comprises a symbolization parameter determiner 144 connected between the output of the desymbolizer and the parameter input of the desymbolizer 124. The determiner 144 is configured to determine the symbolization parameter 46 (which may be derived from the desymbolized segment or the portion desymbolized/processed/decoded so far) for the current transform coefficient from previously processed transform coefficients via the function 52.

The extractor 120, the de-symbolizer 124, and the symbolization parameter determiner 144 are configured to process the transform coefficients of different transform blocks in sequence, as described above. That is, the scan 140 may traverse in opposite directions within the transform block 10. Several scans may be performed, for example, for different symbolized segments, i.e., prefixes and suffixes.

The function parameters vary depending on the size of the transform block of the current transform coefficient, the type of information component of the transform block of the current transform coefficient, and/or the frequency portion in which the current transform coefficient is located within the transform block.

The apparatus may be configured such that the function defining the relationship between previously decoded transform coefficients on the one hand and the symbolization parameters on the other hand is g(f(x)), which function has been described above.

As also discussed above, spatial determination of previously processed transform coefficients in terms of relative spatial arrangement with respect to the current transform coefficient may be used.

The apparatus can operate very easily and quickly because the extractor 120 can be configured to extract the set of symbols from the data stream directly or using entropy decoding with a fixed probability distribution.The parameterizable symbolization scheme can be such that the set of symbols is a Rice code and the symbolization parameters are Rice parameters.

In other words, the de-symbolizer 124 can be configured to restrict the symbolization scheme to level intervals outside the range interval 20 of the transform coefficient, such as 18 or 138, so that the set of symbols represents a prefix or suffix relative to the rest of the overall symbolization of the current transform coefficient, such as 44 and 132 or 142. For other symbols, they can also be extracted from the data stream directly or using entropy decoding using a fixed probability distribution, but Figures 1 to 9 show that entropy coding using context adaptability can also be used.

The apparatus of FIG. 10 may be used as the apparatus 102 in the picture decoder 102 of FIG. 8 .

For the sake of completeness, FIG. 12 shows an apparatus for encoding a plurality of transform coefficients of different transform blocks, each having a transform coefficient level, into a data stream 32 , assembled to the apparatus of FIG. 10 .

The apparatus of FIG. 12 comprises a symbolizer configured to map transform coefficient levels onto a set of symbols or a sequence of symbols according to a symbolization scheme for a current transform coefficient, the symbolization scheme being parameterizable according to a symbolization parameter.

Inserter 154 is configured to insert a set of signs of the current transform coefficients into the data stream 32 .

The symbolization parameter determiner 156 is configured to determine the symbolization parameter 46 for the current transform coefficient depending on the previously processed transform coefficient via the function 52 which is parameterizable by means of a function parameter, and for this purpose it can be connected between the output of the interpolator 152 and the parameter input of the symbolizer 150, or alternatively between the output and the input of the symbolizer 150.

The inserter 154, the symbolizer 150 and the symbolization parameter determiner 156 can be configured to process the transform coefficients of different transform blocks in sequence, and the function parameters change depending on the size of the transform block of the current transform coefficient, the information component type of the transform block of the current transform coefficient and/or the frequency part of the current transform coefficient within the transform block.

As described above with respect to the decoding apparatus of FIG. 10 , the apparatus of FIG. 12 can be configured such that the function defining the relationship between previously decoded transform coefficients on the one hand and symbolization parameters on the other hand is g(f(x)), and the previously processed transform coefficients can be spatially determined based on their relative spatial arrangement with respect to the current transform coefficient. The inserter can be configured to insert the set of symbols into the data stream directly or using entropy coding with a fixed probability distribution, and the symbolization scheme can be such that the set of symbols is a Rice code and the symbolization parameters are Rice parameters. The symbolizer can be configured to restrict the symbolization scheme to level intervals 18 outside the range interval 20 of the transform coefficients, such that the set of symbols represents a prefix or suffix of the rest of the overall symbolization with respect to the current transform coefficient.

As mentioned above, for the preferred implementation of the embodiments of Figures 10 to 12, the context model selection for the first three bins is disabled compared to the embodiments of Figures 1 to 9. For this preferred embodiment, the bins produced by the truncated unary binarization 128 are encoded with a fixed probability of 0.5. In another preferred embodiment, the truncated unary binarization 128 is omitted as shown in Figure 11B and the limits of the Rice interval are adjusted to produce an interval range that is the same as the state of the art (i.e., the left and right limits are subtracted by 3). For this preferred embodiment, the Rice parameter derivation rule is modified compared to the embodiments of Figures 1 to 9. For example, f0 can be used instead of _f1 as the evaluation value _. Further, the input vector can be adjusted to n = {4, 10, 22}.

Another embodiment described below illustrates the possibility of having different templates for context selection/dependence, on the one hand, and for symbolic parameter determination, on the other. That is, the template for the coefficients x _i remains constant for both context selection/dependence and symbolic parameter determination, but the coefficients x _i that are intended to influence f(x) effectively differ between context selection/dependence and symbolic parameter determination by appropriately setting w _i : all coefficients x _i with a weight w _i of zero therefore do not influence f(x), thereby designing the portion of the template where w _i is zero to differ between context selection/dependence, on the one hand, and symbolic parameter determination, on the other, effectively resulting in different "effective templates" for context selection/dependence and symbolic parameter determination. In other words, by setting some w _i to zero for certain template positions i for one of the context selection/dependence and symbolic parameter determination, while setting w _i at certain template positions i to non-zero values for the other, the template for the first of the two is effectively smaller than the template for the second of the two. Furthermore, as already indicated above, the template may contain all transform coefficients of a block, regardless of the position of the currently coded transform coefficient.

For example, see FIG. 13 , which illustrates a transform coefficient block 10 exemplarily consisting of an array of 16x16 transform coefficients 12. The transform coefficient block 10 is subdivided into sub-blocks 200 of 4x4 transform coefficients 12. Thus, the sub-blocks 200 are arranged in a regular 4x4 array. According to this embodiment, for encoding the transform coefficient block 10, a significance map is encoded within the data stream 32 , indicating the positions of the significant transform coefficient levels 12, i.e., transform coefficient levels that are not equal to 0. The transform coefficient level minus one of these significant transform coefficients can then be encoded within the data stream. The encoding of the subsequent transform coefficient levels can be performed as described above, i.e., by a hybrid of context-adaptive entropy coding and variable-length coding using a common parameterizable function to select the context and determine the symbolization parameters. A certain scanning order can be used to sequence or order the significant transform coefficients. An example of this scanning order is shown in FIG13 : subblocks 200 are scanned from the highest frequency (lower right) to DC (upper left), and within each subblock 200, the transform coefficients I2 are scanned before accessing the transform coefficients of the next subblock in the subblock order. This is illustrated by arrow 202, which indicates the subblock scan, and arrow 204, which shows a portion of the actual coefficient scan. A scan index can be transmitted within the data stream 32 to allow selection between several scan paths, respectively scanning the subblocks 200 and/or the transform coefficients I2 within the subblocks. In FIG13 , a diagonal scan is shown for the subblock scan 202 and the transform coefficient I2 scan within each subblock. Thus, at the decoder, the significance map can be decoded, and the transform coefficient levels of the significant transform coefficients can be decoded using the scan order just mentioned and using the above-described embodiment utilizing a parameterizable function. In the description outlined in more detail below, xS and yS denote the subblock column and row, respectively, measured from the DC position (i.e., the upper-left corner of block 10), within which the currently encoded/decoded transform coefficient is located. xP and yP denote the position of the currently encoded/decoded transform coefficient, measured from the upper-left corner (DC coefficient position) of the current subblock (xS, yS). This is illustrated for the upper-right subblock 200 in FIG. 13 . xC and yC denote the currently decoded/encoded transform coefficient position, measured in transform coefficients, from the DC position. Furthermore, because the block size of block 10 in FIG. 13 , i.e., 16x16, was chosen for illustrative purposes only, the embodiments outlined further below use log2TrafoSize as the parameter representing the size of block 10, assuming it is quadratic. log2TrafoSize denotes the base-2 logarithm of the number of transform coefficients within each row of transform coefficients for block 10, i.e., the _log² of the length of the edge of block 10, measured in transform coefficients. CtxIdxInc ultimately selects the context. Furthermore, in the specific embodiment outlined below, it is assumed that the aforementioned significance map indicates coded_sub_block_flag, i.e., a binary syntax element or flag, for the sub-blocks 200 of the block 10 in order to indicate, on a sub-block-by-sub-block basis, whether any valid transform coefficients are located within each sub-block 200, i.e., whether only invalid transform coefficients are located within each sub-block 200. If the flag is zero, then only invalid transform coefficients are located within each sub-block.

Therefore, according to this embodiment, the following is performed by the context adaptive entropy decoder/encoder to select the context of significant_coeff_flag, that is, a flag (which is part of the significance map and a signal of a certain transform coefficient of the sub-block), and coded_sub_block_flag is used to determine whether each coefficient is significant, that is, whether it is non-zero, indicating that each sub-block 200 contains a non-zero transform coefficient.

The inputs to this process are the color component index cIdx, the current coefficient scan position (xC, yC), the scan order index scanIdx, and the transform block size log2TrafoSize. The output of this process is CtxIdxInc.

The variable sigCtx depends on the current position (xC, yC), the color component index cIdx, the transform block size, and the previous decoding bin of the syntax element coded_sub_block_flag. For the derivation of sigCtx, the following applies.

-If log2TrafoSize is equal to 2, sigCtx is derived using ctxIdxMap[] as specified in Table 1 below.

sigCtx＝ctxIdxMap[(yC＜＜2)+xC]

- Otherwise, if xC+yC is equal to 0, then sigCtx is derived as follows.

sigCtx=0

Otherwise, sigCtx is derived using the previous value of coded_sub_block_flag as follows.

- The horizontal and vertical sub-block positions xS and yS are set equal to (xC>>2) and (yC>>2), respectively.

-The variable prevCsbf is set equal to 0.

-When xS is less than (1＜＜(log2TrafoSize-2))-1, the following applies.

prevCsbf+=coded_sub_block_flag[xS+1][yS]

-When yS is less than (1＜＜(log2TrafoSize-2))-1, the following applies.

prevCsbf+＝(coded_sub_block_flag[xS][yS+1]＜＜1)

- The interior subblock positions xP and yP are set equal to (xC&3) and (yC&3) respectively.

-The variable sigCtx is derived as follows.

- If prevCsbf is equal to 0, the following applies.

sigCtx＝(xP+yP＝＝0)? 2:(xP+yP＜3)? 1:0

- Otherwise, if prevCsbf is equal to 1, the following applies.

sigCtx＝(yP＝＝0)? 2:(yP==1)? 1:0

- Otherwise, if prevCsbf is equal to 2, the following applies.

sigCtx＝(xP＝＝0)? 2:(xP==1)? 1:0

- Otherwise, (prevCsbf is equal to 3), then the following applies.

sigCtx=2

-The variable sigCtx is modified as follows.

- If cIdx is equal to 0, the following applies.

-When (xS+yS) is greater than 0, the following applies.

sigCtx+=3

-The variable sigCtx is modified as follows.

- If log2TrafoSize is equal to 3, the following applies.

sigCtx+=(scanIdx==0)? 9:15

- Otherwise, the following applies.

sigCtx+=21

- Otherwise, (cIdx is greater than 0), the following applies.

- If log2TrafoSize is equal to 3, the following applies.

sigCtx+=9

- Otherwise, the following applies.

sigCtx+=12

The context-inclusive increment CtxIdxInc is derived as follows using the color component indices cIdx and sigCtx.

- If cIdx is equal to 0, then CtxIdxInc is derived as follows.

ctxIdxInc=sigCtx

- Otherwise, (cIdx is greater than 0), CtxIdxInc is derived as follows.

ctxIdxInc＝27+sigCtx

Table 1 - Specifications of ctxIdxMap[i]

i 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ctxIdxMap[i] 0 1 4 5 2 3 4 5 6 6 8 8 7 7 8

As described above, for each significant transform coefficient, a further set of syntax elements or symbols may be conveyed within the data stream to indicate its level. According to the embodiment outlined below, for a significant transform coefficient, the following set of syntax elements or transform coefficients is transmitted: coeff_abs_level_greater1_flag, coeff_abs_level_greater2flag (optional), and coeff_abs_level_remaining, such that the currently encoded/decoded significant transform coefficient level TransCoeffLevel is:

TransCoeffLevel=(coeff_abs_level_remaining+baseLevel)*(1-2*coeff_sign_flag])

in

baseLevel=1+coeff_abs_level_greater1_flag+coeff_abs_level_greater2_flag

Note that significant_coeff_flag is by definition 1 for significant transform coefficients and, therefore, can be considered as part of the coded transform coefficient, ie, part of its entropy coded sign.

The context adaptive entropy decoder/encoder may, for example, perform context selection for coeff_abs_level_greater1_flag as follows. For example, the current subblock scan index i may increase in the DC direction along the scan path 202, and the current coefficient scan index n may increase within each subblock along the scan path 204, where the currently encoded/decoded transform coefficient position is located within each subblock, wherein, as outlined above, different possibilities exist for the scan paths 202 and 204, and they are actually variable according to the index scanIdx.

The inputs to the process of selecting the context of coeff_abs_level_greater1_flag are the color component index cIdx, the current subblock scan index i, and the current coefficient scan index n within the current subblock.

The output of this process is CtxIdxInc.

The variable ctxSet specifies the current context set and for its derivation, the following applies.

If this procedure is called for the first time for the current sub-block scan index i, then the following applies.

-The variable ctxSet is initialized as follows.

- If the current sub-block scan index i is equal to 0 or cIdx is greater than 0, the following applies.

ctxSet=0

- Otherwise (i is greater than 0 and cIdx is equal to 0), the following applies.

ctxSet=2

-The variable lastGreater1Ctx is derived as follows.

If the current subblock with scan index i is the first subblock to be processed in this section for the current transform block, the variable lastGreater1Ctx is set equal to 1.

Otherwise, the variable lastGreater1Ctx is set equal to the value of greater1Ctx, which was derived during the last call of the procedure specified in this section for the syntax element coeff_abs_level_greater1_flag for the previous subblock with scan index i+1.

-When lastGreater1Ctx is equal to 0, ctxSet is incremented by 1 as follows.

ctxSet＝ctxSet+1

-The variable greater1Ctx is set equal to 1.

- Otherwise (the process is not called for the current sub-block scan index i in the first time), the following applies.

-The variable ctxSet is set equal to the variable ctxSet that has been derived during the last call to the procedure specified in this section.

-The variable greater1Ctx is set equal to the variable greater1Ctx that has been derived during the last call to the procedure specified in this section.

- When greater1Ctx is greater than 0, the variable lastGreater1Flag is set equal to the syntax element coeff_abs_level_greater1_flag used during the last call to the procedure specified in this section and greater1Ctx is modified as follows.

- If lastGreater1Flag is equal to 1, greater1Ctx is set equal to 0.

- Otherwise (lastGreater1Flag is equal to 0), greater1Ctx is incremented by 1.

The context index increment CtxIdxInc is derived using the current context set ctxSet and the current context greater1Ctx as follows.

ctxIdxInc=(ctxSet*4)+Min(3,greater1Ctx)

When cIdx is greater than 0, CtxIdxInc is modified as follows.

ctxIdxInc＝ctxIdxInc+16

The process of selecting the context of coeff_abs_level_greater2_flag can be made the same as coeff_abs_level_greater2_flag, with the following differences:

The context index increment CtxIdxInc is set equal to the variable ctxSet as follows.

ctxIdxInc＝ctxSet

When cIdx is greater than 0, CtxIdxInc is modified as follows.

ctxIdxInc＝ctxIdxInc+4

For symbolication parameter selection, the following is performed by the symbolication parameter determiner to determine the symbolication parameters which include cLastAbsLevel and cLastRiceParam here.

The input to this process is the request for the syntax element coeff_abs_level_remaining[n] to be binarized and baseLevel.

The output of this process is the binarization of syntax elements.

The variables cLastAbsLevel and cLastRiceParam are derived as follows.

-If n is equal to 15, cLastAbsLevel and cLastRiceParam are set equal to 0.

Otherwise (n is less than 15), cLastAbsLevel is set equal to baseLevel + coeff_abs_level_remaining[n+1] and cLastRiceParam is set equal to the value of cRiceParam derived during the last invocation of the binarization process specified in this section for the syntax element coeff_abs_level_remaining[n+1] for the same transform block.

The variable cRiceParam is derived from cLastAbsLevel and cLastRiceParam as follows:

cRiceParam＝Min(cLastRiceParam+(cLastAbsLevel＞(3*(1＜＜cLastRiceParam))?1:0),4)

The variable cTRMax is derived from cRiceParam as:

cTRMax＝4＜＜cRiceParam

The coeff_abs_level_remaining binarization can consist of a prefix part (when present) and a suffix part.

The binarized prefix part is derived by calling the Rice binarization process of, for example, prefix part Min(cTRMax, coeff_abs_level_remaining[n]).

When the prefix bin string is equal to a bit string of length 4, e.g., all bits are equal to 1, the bin string may consist of a prefix bin string and a suffix bin string. The suffix bin string may be derived using the exponential Golomb k-order binarization of the suffix part (coeff_abs_level_remaining[n]-cTRMax), where the exponential Golomb k-order is set equal to cRiceParam+1, for example.

It should be noted that the above-described embodiment can be modified. For example, the dependency on the color component index cIdx can be retained. For example, only one color component should be considered. Furthermore, all specific values can be changed. To this extent, the example just outlined is to be interpreted broadly so as to also incorporate variations.

In the above example, the embodiments outlined above can be advantageously used in the following manner: In particular, the symbolization parameters CtxIdxInc and coeff_abs_level_remaining that determine coeff_abs_level_greater1_flag are coordinated using the above functions f and g by setting the function parameters in the following manner.

To this end, FIG13 exemplarily shows a "current transform coefficient" indicated by a cross 206. This is representative of any transform coefficient associated with any syntax element mentioned later. It is located at (xP, yP) = (1, 1) and (xC, yC) = (1, 5) within the current subblock (xS, yS) = (0, 1). The right neighboring subblock is at (xS, yS) = (1, 1), the bottom neighboring subblock is at (xS, yS) = (0, 2), and the previously coded subblock follows the scan path 202. Here, by way of example, a diagonal scan 202 is shown, and the coded/decoded subblock immediately preceding the current subblock is at (xS, yS) = (1, 0).

We rewrite the formula of the commonly used parameterizable function again

f(x)＝∑ _i w _i ×h(x _i )×δ( _xi , t) (2)

The following can be calculated by the entropy encoding/decoding apparatus for the context of selecting the significant_coeff_flag of the current coefficient 206. That is, it can use function (1), where (2) has function parameters t, h, and w set as follows:

For function (2), for all x _i in the adjacent subblocks to the right and below the current subblock, w _i = 1, and w _i = 0 elsewhere in the block 10;

For all x _i in the neighboring subblocks to the right of the current subblock, h(x _i )=1; if any, they are also previously scanned in the subblock scan 202; if more than one scan 202 is available, all of them can make (independent of scanIdx) that the neighboring subblock to the right has coefficients encoded/decoded before the current subblock;

For all x _i in the adjacent subblocks below the current subblock previously scanned in the subblock scan, h(x _i )=2 ⁴ +1 (independent of scanIdx);

Otherwise h( _xi ) = 0;

t = 1;

If the value of f is equal to 0, it indicates that the adjacent sub-blocks to the right and below the current sub-block Nachbarn do not include any valid transform coefficients;

If the value of f is between 1 and 16 (inclusive), this corresponds to the fact that coded_sub_block_flag is equal to 1 in the right adjacent sub-block;

If the value of f is a multiple of 2 ⁴ +1 (without remainder), this corresponds to the fact that coded_sub_block_flag is equal to 1 in the bottom adjacent subblock;

If the value of f is a multiple of 2 ⁴ +1 (but with a remainder), this means that coded_sub_block_flag is equal to 1 for two adjacent subblocks, one to the right of the current subblock and one below the current subblock;

For function (1), n is set as follows, where d _f is 3:

n＝(0，2 ⁴ ，m)

in

By this measure, the variable component of the context index is determined using g(f), where the above function parameters are based on the already encoded/decoded coefficients.

For the context in which coeff_abs_greater1_flag is selected, the following can be calculated by the entropy encoding/decoding apparatus. That is, it can use function (1), where (2) has function parameters set as follows:

For function (2), the parameters are set as follows:

For all x _i in the immediately preceding subblock and the current subblock, w _i = 1, and is zero for all others.

For all x _i in the current sub-block, h(x _i )＝1, where |x _i |＝1

For all x _i in the current sub-block, h(x _i )＝2 ⁴ , where |x _i |＞1

For all x _i in the immediately preceding subblock, h(x _i )=2 ¹⁶

t＝2

For function (1), n is set as follows and d _f is 8:

n=(0, ¹ , 2, 2 ⁴ , 2 ¹⁶ , 2 16 +1 ^{, 2 16} +2, ^{2 16} +2 ⁴ )

For the context where coeff_abs_greater2_flag is selected, the following can be calculated by the entropy encoding/decoding apparatus. Specifically, it can use function (1), where (2) has the function parameters set as described above for coeff_abs_greater2_flag, but _df is 1:

n＝(2 ¹⁶ )

For determining the symbolic parameter of coeff_abs_level_remaining, the symbolic parameter determiner may use the common function (1), where the function parameters are set as follows:

For function (2), the parameters are set as follows:

For all x _i in the current subblock, w _i = 1, but zero elsewhere

For a coefficient x _i that was recently accessed according to the intra coefficient scan 204 (for which coeff_abs_level_remaining has been encoded), i.e., whose level falls within the interval corresponding to the symbolization scheme, h(x _i )=1;

h( _xi )＝0 in other places of the template

t＝0

For function (1), n is set as follows:

For the most recently mentioned coefficient accessed according to the internal coefficient scan 204 , n=(2 ^m ), where k is a symbolization parameter, such as a Ricean parameter. Using the resulting g(f), the symbolization parameter of the current coefficient 206 is determined.

The following syntax can be used to pass the syntax elements just outlined.

The syntax indicating the level of the transform coefficient consists of coeff_abs_level_remaining and baseLevel, where baseLevel is composed of 1 + coeff_abs_level_greater1_flag[n] + coeff_abs_level_greater2_flag[n]. 1 is used because at this position (or when the level is reconstructed in the decoder), the syntax element is significant_coeff_flag = 1. The "first set" then consists of the TU code (Rice code with parameterization equal to 0), from which the first three syntax elements are formed. The "second set" then forms the syntax element coeff_abs_level_remaining.

Since the boundary shifts between the "first set" and the "second set", the maximum value is defined by coeff_abs_greater1_flag, coeff_abs_greater2_flag or by significant_coeff_flag, so the branching depends on the syntax element in the table.

The above setting of function parameters is still somewhat purposeful in the following text.

g(f) forms the result of the sum of adjacent coefficients and uses the derived context and desymbolization parameters, where later modifications can be performed depending on the spatial position.

g(x) takes a single value. This value corresponds to the result of the function f(x). Knowing this, we can deduce the context selection and the parameterization of the Rice parameter.

significant_coeff_flag: Since h itself can be a function of x, f(x) or any other function can be chained again and again. For all positions in the right 4x4 subblock, the function f(x), where _wi = 1, t = 1, and h is configured like f(x) but not inverted, so that the final value is 0 or 1, that is, h(x) = min(1, f(x)).

Equivalently, for the second entry, this applies to the bottom 4x4 subblock. Then, prevCsbf = h ₀ + 2×h ₁ , where prefCsbf may also be a function h within f(x).

If t = ∞ is set, the value of the syntax element coded_sub_block_flag can be derived. Thus, a value between 0 and 3 is obtained as the result of the outermost f(x). The parameter n of g(x) can then be (xP+yP), xP, yP, or (0,0). If f(x) = 0 is obtained, then n = (xP+yP, xP+yP+3), for f(x) = 1 n = (yP, yP+1), for f(x) = 2 n = (xP, xP+1), and for f(x) = 3 n = (0,0). It can be said that f(x) can be directly evaluated to determine n. The remaining formulas above only describe the adaptation based on luma/chroma and the further dependence on global position and scanning. For a pure 4x4 block, f(x) can be configured so that the value of prevCsbf = 4 (which can also be different) and therefore the mapping table can be reproduced.

coeff_abs_level_greater1_flag: Here, the evaluation of the subblocks is similar, where only the previous subblock is evaluated. The result is, for example, 1 or 2 (which can only be two different values), where t=2. This corresponds to the selection of the base index according to the already decoded level in the previous subblock. A direct dependency on the level located within the subblock can thus be obtained. Effectively, a switching on of one index (starting from 1 and limited to 3) is performed when decoding 0 and it is set to 0 as soon as 1 is decoded. If this arrangement is not taken into account, the parameterization can be performed as follows, starting from 0. For all levels w _i = 1 and t = 3 in the same subblock, f(x) provides the number of levels for which coeff_abs_greater1_flag = 1. For the further function f(x), t = 2, i.e. the number of positions of the coding syntax element coeff_abs_greater1_flag. The first function is constrained to h ₀ = f(x) = min(f ₀ (x), 2), and the second function is constrained to h ₁ = f(x) = max(f ₁ (x), 1). All are associated with the delta function (0 if h ₁ = 1, h ₀ otherwise). For coeff_abs_greater2_flag, only the derivation of the set is used ( _wi is set to 0 for chained inner functions).

coeff_abs_level_remaining: The selection is limited to the current subblock and n is derived as described above.

With respect to the embodiment just outlined, the following considerations apply. Specifically, as described above, different possibilities exist for defining a template: the template can be a moving template, whose position is determined by the position of the current coefficient 206. An overview of this exemplary moving template is depicted in FIG13 by dashed line 208. The template consists of the current subblock within which the current coefficient 206 is located, the neighboring subblocks to the right and below the current subblock, and one or more subblocks, if any (one of which can be selected using the scan index as explained above), that precede the current subblock in the subblock scan 202 or any subblock scan 202. Alternatively, the template 208 can simply contain all transform coefficients 12 of the block 10.

In the above example, there are further different possibilities for selecting the values of h and n. These values can therefore be set in different ways. This is also somewhat true for w _i , as far as these weights are concerned, which are set to 1. They can also be set to another non-zero value. They do not even have to be equal to each other. Because w _i is multiplied by h( _xi ), the same product value can be achieved by setting non-zero w _i in different ways. Moreover, the symbolization parameters do not necessarily have to be Rice parameters, or to put it differently, the symbolization scheme is not limited to the Rice symbolization scheme. As for the context index selection, refer to the above description, in which it has been noted that the final context index can be obtained by adding the context index obtained using the function g(f) to some offset index, which is, for example, specific to each type of syntax element, that is, specific to significant_coeff_flag, coeff_abs_level_greater1_flag and coeff_abs_level_greater2_flag.

Although several aspects have been described in the context of an apparatus, it is clear that these aspects also represent descriptions of corresponding methods, where blocks or apparatuses correspond to method steps or features of method steps. Similarly, aspects described in the context of method steps also represent descriptions of corresponding blocks or items or features of corresponding apparatuses. Some or all of the method steps may be performed by (or using) hardware devices, such as, for example, microprocessors, programmable computers, or electronic circuits. In certain embodiments, one or more of the most important method steps may be performed by such devices.

Depending on the requirements of certain implementations, embodiments of the present invention have been implemented in hardware or software. Implementation can be performed using a digital storage medium, such as a floppy disk, DVD, Blu-ray disc, CD, ROM, PROM, EPROM, EEPROM, or flash memory, having stored thereon electronically readable control signals that cooperate (or can cooperate) with a programmable computer system to perform the respective methods. The digital storage medium can therefore be a computer-readable medium.

Some embodiments according to the invention comprise a data carrier having electronically readable control signals, which are capable of cooperating with a programmable computer system, such that one of the methods described herein is performed.

Generally, the embodiments of the present invention can be implemented as a computer program product having a program code, which, when the computer program product runs on a computer, is operable to perform one of the methods. The program code can be stored on a machine-readable carrier, for example.

Other embodiments comprise the computer program for performing one of the methods described herein, stored on a machine readable carrier.

In other words, an embodiment of the inventive method is, therefore, a computer program having a program code for performing one of the methods described herein, when the computer program runs on a computer.

A further embodiment of the inventive method is, therefore, a data carrier (or a digital storage medium or a computer-readable medium) comprising, recorded thereon, the computer program for performing one of the methods described herein. The data carrier, the digital storage medium or the recorded medium are typically tangible and/or non-transferable.

A further embodiment of the inventive method is, therefore, a data stream or a sequence of signals representing the computer program for performing one of the methods described herein.The data stream or the sequence of signals can, for example, be configured to be transmitted via a data communication connection, for example via the Internet.

A further embodiment comprises a processing means, for example a computer or a programmable logic device, configured to or adapted to perform one of the methods described herein.

A further embodiment comprises a computer having installed thereon the computer program for performing one of the methods described herein.

A further embodiment according to the present invention comprises an apparatus or system configured to deliver (e.g. electronically or optically) a computer program for performing one of the methods described herein to a receiver. The receiver may be, for example, a computer, a mobile device, a memory device, etc. The apparatus or system may, for example, comprise a file server for delivering the computer program to the receiver.

In some embodiments, a programmable logic device (e.g., a field programmable gate array) may be used to perform some or all of the functionality of the methods described herein. In some embodiments, a field programmable gate array may cooperate with a microprocessor to perform one of the methods described herein. Typically, such methods are preferably performed by hardware.

The above embodiments are intended to illustrate the principles of the present invention only. It should be understood that modifications and variations of the configurations and details described herein will be apparent to those skilled in the art. Accordingly, it is intended that the present invention be limited only by the scope of the appended patent claims and not by the specific details presented in the description and explanation of the embodiments herein.

Claims (44)

1. An apparatus for decoding a plurality of transform coefficients (12) having transform coefficient levels from a data stream (32), comprising: a context-adaptive entropy decoder (80) configured to entropy decode a first set of one or more symbols (44) from the data stream (32) for a current transform coefficient (x); a de-symbolizer (82) configured to map said first set of one or more symbols (44) onto transform coefficient levels within a first level interval (16) according to a first symbolization scheme; an extractor (84) configured to extract a second set (42) of symbols from the data stream (32) if the transform coefficient level to which the first set of one or more symbols is mapped according to the first symbolization scheme is a maximum level of the first level interval (16), wherein the desymbolizer (82) is configured to map the second set of symbols (42) to positions within a second level interval (18) according to a second symbolization scheme, the second symbolization scheme being parameterizable according to a symbolization parameter, wherein the context adaptive entropy decoder (80) is configured to use a context in dependence on previously decoded transform coefficients during entropy decoding of at least one predetermined symbol of the first set (44) of one or more symbols from the data stream (32) via a function parameterizable by a function (52) parameter, wherein the function parameter is set to a first setting, and The apparatus further comprises a symbolization parameter determiner (86) configured to determine a symbolization parameter (46) based on the previously decoded transform coefficients via a function (52) in which the function parameter is set to a second setting, if the transform coefficient level to which the first set of one or more symbols (44) is mapped according to the first symbolization scheme is the maximum level of the first level interval (16), The extractor, the de-symbolizer and the symbolization parameter determiner are configured to process transform coefficients of different transform blocks using a zigzag or raster scan. 2. The apparatus according to claim 1 , wherein the apparatus is configured such that a function defining a relationship between, on the one hand, the previously decoded transform coefficients and a context index offset number for indexing the context, and, on the other hand, the symbolization parameter is: g(f(x)), where, and in, and in, t, w _i and form the function parameters, where t is input as a constant, x={x ₁ ,...,x _d }, i∈{1...d} where x _i represents the previously decoded transform coefficient i, w _i are weight values, each of which may be equal to one or not equal to one, and h is a constant or a function of x _i . 3. The apparatus of claim 2 , wherein the context adaptive entropy decoder is configured such that the dependency of the context from the previously decoded transform coefficients is determined via the function: such that, if the transform coefficient level of the previously decoded transform coefficient i is within the first level interval, x _i is equal to the transform coefficient level of the previously decoded transform coefficient i, and is equal to the maximum level of the first level interval if the transform coefficient level of the previously decoded transform coefficient i is within the second level interval, or Let x _i be equal to the transform coefficient level of the previously decoded transform coefficient i, regardless of whether the transform coefficient level of the previously decoded transform coefficient i is within the first level interval or the second level interval. 4. The apparatus of claim 2 , wherein the symbolization parameter determiner is configured such that the dependency of the symbolization parameter on the previously decoded transform coefficient is such that x _i is equal to the transform coefficient level of the previously decoded transform coefficient i via a function, regardless of whether the transform coefficient level of the previously decoded transform coefficient i is within the first level interval or the second level interval. The apparatus according to claim 2 , wherein the apparatus is configured such that n ₁ ≤ ... ≤ n _df . The apparatus of claim 2 , wherein the apparatus is configured such that h is | _xi |−t. 7 . The apparatus of claim 1 , wherein the apparatus is configured to spatially determine the previously decoded transform coefficients as a function of a relative spatial arrangement of the transform coefficients with respect to a current transform coefficient. 8. The apparatus according to claim 1 , wherein the apparatus is configured to extract information about a position of a last non-zero transform coefficient among transform coefficients of a transform coefficient block from the data stream ( 32 ) along a predetermined scanning order ( 14 ), wherein the plurality of transform coefficients include transform coefficients from the last non-zero transform coefficient along the scanning order to a DC transform coefficient of the transform coefficient block. 9. The apparatus of claim 8 , wherein the desymbolizer is configured to use a modified first symbolization scheme for mapping a first set of one or more symbols for the last non-zero transform coefficient, wherein only non-zero transform coefficient levels within the first level interval are involved, while it is presumed that a zero level does not apply to the last transform coefficient. 10. The apparatus of claim 8 , wherein the context adaptive entropy decoder is configured to use a separate set of contexts for entropy decoding the first set of one or more symbols of the last non-zero transform coefficient, the separate set being independent of contexts used in entropy decoding the first set of one or more symbols different from the last non-zero transform coefficient. 11 . The apparatus of claim 8 , wherein the context adaptive entropy decoder traverses the plurality of transform coefficients in a reverse scanning order from the last non-zero transform coefficient of the transform coefficient block to the DC transform coefficient. 12. An apparatus according to claim 1, wherein the apparatus is configured to decode the plurality of transform coefficients from the data stream in two scans, wherein the context adaptive entropy decoder is configured to entropy decode the first set of symbols of the transform coefficients from the data stream in an order corresponding to the first scan of the transform coefficients, and wherein the extractor is configured to subsequently extract from the data stream a second set of symbols of the transform coefficients mapped to the maximum level of the first level interval in an order corresponding to the mapping of the first set of symbols to the transform coefficients at the maximum level of the first level interval. 13. The apparatus of claim 1 , wherein the apparatus is configured to decode the plurality of transform coefficients sequentially from the data stream in a scan, wherein the second set of symbols is interspersed within the data stream between the first set of symbols for the transform coefficients, and wherein the context adaptive entropy decoder and the extractor are configured to extract, for each transform coefficient in a scan order of the scan, the second set of symbols that map from the data stream to the respective transform coefficients at the maximum level of the first level interval immediately after the context adaptive entropy decoder entropy decodes, from the data stream, the first set of symbols that map to the respective transform coefficients at the maximum level of the first level interval. 14. The apparatus of claim 1, wherein the extractor is configured to extract the second set of symbols from the data stream directly or using entropy decoding with a fixed probability distribution. 15. The apparatus of claim 1, wherein the first symbolization scheme is a truncated unary binarization scheme. 16. The apparatus of claim 1, wherein the second symbolization scheme is such that the second set of symbols is a Rice code. 17. The apparatus of claim 1, wherein the data stream has a depth map encoded therein. 18. A picture decoder comprising an apparatus according to claim 1, wherein the picture decoder is configured to, during decoding of a picture, re-transform blocks of the picture from transform coefficient blocks, wherein the apparatus is configured to sequentially decode multiple transform coefficients of a transform coefficient block on a transform coefficient block-by-transform coefficient block basis using functions of transform coefficient blocks of different sizes, transform coefficient blocks of different sizes and/or transform coefficient blocks of different information component types. 19. A picture decoder according to claim 18, wherein the device is configured to use different sets of contexts for different frequency parts of the transform coefficient block, for transform coefficient blocks of different sizes and/or for transform coefficient blocks of different information component types, wherein the context of the current transform coefficient is selected based on the previously decoded transform coefficient. 20. An apparatus for encoding a plurality of transform coefficients having transform coefficient levels into a data stream (32), comprising: The symbolizer (34) is configured to If the transform coefficient level of the current transform coefficient is within a first level interval (16), mapping the current transform coefficient onto a first set of one or more symbols according to a first symbolization scheme, and If the transform coefficient level of the current transform coefficient is within a second level interval (18), mapping the current transform coefficient to a combination of a second set of symbols and a third set of symbols according to a second symbolization scheme, the maximum level of the first level interval (16) being mapped to the second set of symbols according to the first symbolization scheme, the third set of symbols being dependent on the position of the transform coefficient level of the current transform coefficient within the second level interval (18), the second symbolization scheme being parameterizable according to a symbolization parameter (46); a context adaptive entropy encoder (36) configured to entropy encode the first set of one or more symbols into the data stream if the transform coefficient level of the current transform coefficient is within the first level interval, and to entropy encode the second set of one or more symbols into the data stream if the transform coefficient level of the current transform coefficient is within the second level interval, wherein the context adaptive entropy encoder is configured to use a context in dependence on a previously encoded transform coefficient via a function parameterizable by a function parameter set to a first setting during entropy encoding of at least one predetermined symbol of the second set of one or more symbols into the data stream; a symbolization parameter determiner (38) configured to determine, if the transform coefficient level of the current transform coefficient is within the second level interval, the symbolization parameter (46) for mapping onto the third set of symbols from the previously encoded transform coefficients via the function parameter being set to a second setting; and an inserter (40) configured to insert the third set of symbols into the data stream if the transform coefficient level of the current transform coefficient is within the second level interval, The symbolizer and the symbolization parameter determiner are configured to process transform coefficients of different transform blocks using a zigzag or raster scan. 21. The apparatus according to claim 20, wherein the apparatus is configured such that the function defining the relationship between the previously coded transform coefficients and the context index number (56) indexing the context on the one hand, and the symbolization parameter (46) on the other hand is g(f(x)), where, and in, and in, t, w _i and form the function parameters, where t is input as a constant, x = {x ₁ , ..., x _{d }} , where i∈{1...d} represents the previously coded transform coefficient i, w _i are weight values, each of which may be equal to one or not equal to one, and h is a constant or a function of x _i . 22. The apparatus of claim 21, wherein the context adaptive entropy encoder (36) is configured such that the dependency of the context from the previously encoded transform coefficients is determined via the function such that x _i is equal to the transform coefficient level of the previously encoded transform coefficient i if the transform coefficient level is within the first level interval, and is equal to the maximum level of the first level interval (16) if the transform coefficient level of the previously encoded transform coefficient i is within the second level interval (18), or Let x _i be equal to the transform coefficient level of the previously encoded transform coefficient i, regardless of whether the transform coefficient level of the previously encoded transform coefficient i is within the first level interval or the second level interval. 23. The apparatus of claim 21 , wherein the symbolization parameter determiner (38) is configured such that the dependency of the symbolization parameter on the previously encoded transform coefficients is determined via the function: Let x _i be equal to the transform coefficient level of the previously encoded transform coefficient i, regardless of whether the transform coefficient level of the previously encoded transform coefficient i is within the first level interval or the second level interval. 24. The apparatus of claim 21, wherein the apparatus is configured such that 25. The apparatus of claim 21, wherein the apparatus is configured such that h is |xi _| - t. 26. The apparatus of claim 20, wherein the apparatus is configured to spatially determine the previously encoded transform coefficients as a function of a relative spatial arrangement of the transform coefficients with respect to the current transform coefficients. 27. An apparatus according to claim 20, wherein the apparatus is configured to determine a position of a last non-zero transform coefficient among transform coefficients of a transform coefficient block along a predetermined scanning order and insert information about the position into the data stream, wherein the plurality of transform coefficients include transform coefficients from the last non-zero transform coefficient to the beginning of the predetermined scanning order. 28. The apparatus of claim 27, wherein the symbolizer is configured to use a modified first symbolization scheme for symbolizing a last transform coefficient, wherein only non-zero transform coefficient levels within the first level interval are involved, while it is presumed that a zero level does not apply to the last transform coefficient. 29. The apparatus of claim 27 , wherein the context adaptive entropy encoder is configured to use a separate set of contexts for entropy encoding the first set of one or more symbols of the last non-zero transform coefficient, the separate set being independent of contexts used in entropy encoding the first set of one or more symbols different from the last non-zero transform coefficient. 30. The apparatus of claim 27, wherein the context adaptive entropy encoder traverses the plurality of transform coefficients in a reverse scanning order from the last non-zero transform coefficient to a DC transform coefficient of the transform coefficient block. 31. An apparatus according to claim 20, wherein the apparatus is configured to encode the plurality of transform coefficients into the data stream in two scans, wherein the context adaptive entropy encoder is configured to entropy encode the first set and the second set of symbols of the transform coefficients into the data stream in an order corresponding to the first scan of the transform coefficients, and wherein the inserter is configured to subsequently insert the third set of symbols of the transform coefficients having the transform coefficient levels within the second level interval into the data stream in an order corresponding to the occurrence of the transform coefficients having the transform coefficient levels within the second level interval in the second scan of the transform coefficients. 32. An apparatus according to claim 20, wherein the apparatus is configured to encode the plurality of transform coefficients into the data stream sequentially in a scan, wherein the context adaptive entropy encoder and the inserter are configured to, for each transform coefficient in the scan order of the scan, insert the third set of symbols of the respective transform coefficients having transform coefficient levels within the second level interval into the data stream immediately after the context adaptive entropy encoder entropy encodes the second set of one or more symbols of the respective transform coefficients having transform coefficient levels within the second level interval into the data stream, so that the third set of symbols is inserted into the data stream between the first set and the second set of symbols of the transform coefficients. 33. The apparatus of claim 20, wherein the inserter is configured to insert the third set of symbols into the data stream directly or using entropy coding with a fixed probability distribution. 34. The apparatus of claim 20, wherein the first symbolization scheme is a truncated unary binarization scheme. 35. The apparatus of claim 20, wherein the second symbolization scheme is such that the third set of symbols is a Rice code. 36. A picture encoder comprising an apparatus according to claim 20, wherein the picture encoder is configured to transform blocks of the picture into transform coefficient blocks during encoding of the picture, wherein the apparatus (62) is configured to encode a plurality of transform coefficients of the transform coefficient blocks on a transform coefficient block-by-transform coefficient block basis using functions (52) of blocks of different sizes. 37. The picture encoder of claim 36, wherein the apparatus is configured to use different sets of contexts for different frequency parts of a block of transform coefficients, wherein the context for the current transform coefficient is selected in dependence on the previously encoded transform coefficients. 38. The apparatus of claim 37, wherein the data stream has a depth map encoded therein. 39. A method for decoding a plurality of transform coefficients (12) having transform coefficient levels from a data stream (32), comprising: entropy decoding a first set (44) of one or more symbols from the data stream (32) for a current transform coefficient (x); Desymbolically mapping the first set of one or more symbols (44) to transform coefficient levels within a first level interval (16) according to a first symbolization scheme; extracting a second set (42) of symbols from the data stream (32) if the transform coefficient level to which the first set of one or more symbols is mapped according to the first symbolization scheme is a maximum level of the first level interval (16), wherein the desymbolization mapping comprises mapping the second set of symbols (42) to positions within a second level interval (18) according to a second symbolization scheme, the second symbolization scheme being parameterizable according to a symbolization parameter, Entropy decoding involves entropy decoding at least one predetermined symbol of said first set (44) of one or more symbols from a data stream (32) using a context from previously decoded transform coefficients via a function parameterizable by a function (52) parameter, wherein the function parameter is set to a first setting, and The method further comprises: determining the symbolization parameter (46) from the previously decoded transform coefficients via a function (52) in which the function parameter is set to a second setting, if the transform coefficient level to which the first set of one or more symbols (44) is mapped according to the first symbolization scheme is a maximum level of the first level interval (16), Here, the transform coefficients of different transform blocks are processed using zigzag or raster scanning. 40. The method of claim 39, wherein the data stream has a depth map encoded therein. 41. A method for encoding a plurality of transform coefficients having transform coefficient levels into a data stream (32), comprising: If the transform coefficient level of the current transform coefficient is within a first level interval (16), mapping the current transform coefficient onto a first set of one or more symbols according to a first symbolization scheme, and If the transform coefficient level of the current transform coefficient is within a second level interval (18), mapping the current transform coefficient to a combination of a second set of symbols and a third set of symbols according to a second symbolization scheme, the maximum level of the first level interval (16) being mapped to the second set of symbols according to the first symbolization scheme, the third set of symbols being dependent on the position of the transform coefficient level of the current transform coefficient within the second level interval (18), the second symbolization scheme being parameterizable according to a symbolization parameter (46); Context-adaptive entropy coding, comprising entropy coding a first set of the one or more symbols into the data stream if a transform coefficient level of the current transform coefficient is within the first level interval, and entropy coding a second set of one or more symbols into the data stream if the transform coefficient level of the current transform coefficient is within the second level interval, wherein the context-adaptive entropy coding involves, in entropy coding at least one predetermined symbol of the second set of one or more symbols into the data stream, using a context as a function of a previously encoded transform coefficient via a function parameterizable by a function parameter, wherein the function parameter is set to a first setting; and determining the symbolization parameters (46) for mapping onto the third set of symbols from the previously encoded transform coefficients via a function if the transform coefficient level of the current transform coefficient is within the second level interval, wherein the function parameters are set to a second setting; and inserting the third set of symbols into the data stream if the transform coefficient level of the current transform coefficient is within the second level interval, Here, the transform coefficients of different transform blocks are processed using zigzag or raster scanning. 42. The method of claim 41, wherein the data stream has a depth map encoded therein. 43. A method for decoding a data stream, wherein the method comprises: The data stream into which a plurality of transform coefficients representing a picture are encoded by the method according to claim 41 is received and decoded. 44. A method for decoding a data stream, wherein the method comprises: A data stream into which a plurality of transform coefficients representing a picture are encoded in a manner instructing a decoder to decode the plurality of transform coefficients from the data stream by performing the method according to claim 39 is received and decoded.