Classifications

• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
  • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
  • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
• • G—PHYSICS
  • G10—MUSICAL INSTRUMENTS; ACOUSTICS
  • G10L—SPEECH ANALYSIS TECHNIQUES OR SPEECH SYNTHESIS; SPEECH RECOGNITION; SPEECH OR VOICE PROCESSING TECHNIQUES; SPEECH OR AUDIO CODING OR DECODING
  • G10L19/00—Speech or audio signals analysis-synthesis techniques for redundancy reduction, e.g. in vocoders; Coding or decoding of speech or audio signals, using source filter models or psychoacoustic analysis
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
  • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
  • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
  • H03M7/40—Conversion to or from variable length codes, e.g. Shannon-Fano code, Huffman code, Morse code
  • H03M7/4006—Conversion to or from arithmetic code
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
  • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
  • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
  • H04N19/102—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or selection affected or controlled by the adaptive coding
  • H04N19/13—Adaptive entropy coding, e.g. adaptive variable length coding [AVLC] or context adaptive binary arithmetic coding [CABAC]
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
  • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
  • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
  • H04N19/169—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding
  • H04N19/184—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding the unit being bits, e.g. of the compressed video stream

Definitions

• the present invention relates to coding / decoding processing of digital signals such as speech signals, image signals, or more generally audio and / or video signals, or more generally multimedia signals, for storage and / or transmission.
• lossless compression methods Huffman coding, Golomb-Rice coding, arithmetic coding
• entropy coding compression methods, lossy, resting on a scalar or vector quantization.
• a compression encoder typically comprises: an analysis module 100 of the source to be coded S, a quantization module 101 (of scalar or vector type), followed by a module 102 encoding, while a peer decoder comprises: a decoding module 103, an inverse quantization module 104, and a synthesis module 105.
• Reference 205 illustrates the transmission channel from the encoder to the decoder, which may optionally apply truncation of the bit stream.
• the entropic coding of the planes can advantageously be achieved by a so-called "contextual arithmetic" coder.
• the principle of an arithmetic coder is explained in Witten et al:
• the module 203 encodes the bit planes, one by one, starting with the most significant bit planes to the least significant bit planes. This notion of more or less significant bit planes will be described later with reference to FIG. 3.
• the flow rate that is produced at the output of the encoder is, in general, variable. In what follows, the manner of managing this variable bit rate (modules 200 and 204 of FIG. 2) is not described.
• the bit stream generated by the module 203 is finally transmitted on a channel 205, which can truncate the bit stream (by exploiting the hierarchical nature of the bit stream) or introduce binary errors.
• the demultiplexer-decoder (module 206) reconstructs the bit planes P k , one by one, and decodes the sign bits S that have been transmitted. This decoded information makes it possible to reconstruct (module 207) the signal Y.
• the demultiplexer-decoder (module 206) reconstructs the bit planes P k , one by one, and decodes the sign bits S that have been transmitted. This decoded information makes it possible to reconstruct (module 207) the signal Y.
• bitmap coding The main interest of bitmap coding is that it leads naturally to a hierarchical (or progressive) coding of the signal. Successive approximations of the signal becoming more precise can be reconstructed as we receive the entire bit stream transmitted by the encoder.
• N S.
• the sign bits are represented by the vector bearing the reference sgn in FIG. 3.
• K 3
• P 0 [0,1,1,0,1,1,0,1]
• P 1 [1,1,1,0,0,1,1,0]
• P 2 [0,1,0,0,0,0,1,1]
• S [1,0,0, 0,0,1,1,0].
• the vector P k then represents a plane of bits of weight k.
• P ⁇ -1 represents the most significant bit plane (MSB reference for "Most Significant Bits” in English), while the lower bit plane P 0 represents the plane of the least significant bits (LSB reference for "Least Significant Bits”). " in English).
• step 401 the total number K of bit planes (step 401) is obtained.
• the plane Pk of current index k (step 404) is coded.
• the signs of the new significant coefficients associated with the plane Pk are transmitted.
• the coding is therefore performed on successive bit planes Pk, from the MSB plane to the LSB plane. It is indicated that it is also possible to split the planes Pk into sub-vectors to allow an even more progressive decoding, this fractionation possibly being able to go as far as obtaining sub-vectors of unit size (equal to 1).
• Bit planes of absolute values can then be encoded by adaptive arithmetic coding.
• the planes P k can be coded one by one (independently of each other, sequentially going from the MSB plane to the LSB plane) by adaptive arithmetic coding.
• the adaptation of the probabilities of the symbols (0 and 1) in the coding of a plane Pk uses only the bits that have already been coded in the same plane Pk.
• This type of encoding is given in particular in the document:
• More sophisticated coders do not set the initial frequency of 0 and 1 to 1/2, but store probabilities values in pre-recorded tables that give an initial frequency of 0 and 1 adapted to a certain operating context (eg adapted to the flow, or to the type of source to be coded). At best, the coders of the state of the art therefore require a storage of tables of probabilities of the symbols
• prerecorded tables are usually required to apply Huffman type entropy coding or arithmetic coding.
• State-of-the-art techniques are therefore not very flexible because they require pre-computation and storage of information that must be adapted to particular operating conditions (flow rate, source type). Therefore, it is necessary to anticipate, in the design of coders / decoders, all possible situations, in order to generate such tables. The present invention improves the situation.
• these probabilities are calculated dynamically from an estimate of a distribution of the signal.
• the estimation of the signal distribution is conducted on the signal to be coded, before quantization, in order to have the finest possible estimation of the signal distribution (and not an estimate of the signal distribution). distribution of the depleted signal after quantification).
• the signal having a succession of values each value is decomposed into a plurality of symbol values in a respective plurality of symbol planes.
• the probabilities are calculated for at least one plane and are each aimed at the probability of having, in this plane, a symbol value equal to a given symbol. Preferentially, the probabilities are calculated at least for the plane representing the most significant symbol values.
• the probabilities are further calculated for other planes, taking into account a context defined by symbol values taken in planes representing more significant symbol values.
• each symbol value taken in a plane representing a symbol value more significant than a symbol value in a current plane defines a context value for that value. current plan and for this position.
• the aforementioned probabilities are then calculated for this current plane taking into account a plurality of possible values of the context for this current plane.
• a limited number of possible values of the context is chosen, preferably a number of two, with:
• the invention proposes, unlike the prior art, to dispense with any storage of probability tables, which are instead calculated "in line" (as a function of the signal), and to use an estimate of the density of probabilities of the source to be encoded / decoded (for example represented by a generalized Gaussian model) to dynamically calculate the probabilities of the symbols by planes (for example the probabilities of 0 and 1 for a bit plane).
• the invention can therefore use knowledge of a probability model of the source to be encoded (or decoded), and this to estimate a priori the probabilities of symbols in each plane Pk.
• FIG. 5 shows an example of encoder using, in the sense of the invention, a distribution model of the signal to be encoded, for a coding by bit planes
• - Figure 6 shows a decoder homologous to the encoder of Figure 5
• Figure 7 illustrates the density probability of a generalized Gaussian probability p and shows different calculation intervals ( ⁇ ,)
• - Figure 8 shows the flow diagram of the bitplane coding with an initialization of the probability tables for each plane P k, according to the In the first embodiment
• FIG. 9 shows the flowchart of a homologous decoding of the coding of FIG. 8;
• FIG. 9 shows the flowchart of a homologous decoding of the coding of FIG. 8;
• FIG. 10 shows an example of three-plane binary decomposition and contextual coding for the LSB plane
• FIG. FIG. 11 illustrates the bit planes associated with a strongly harmonic signal, as well as a histogram H of this signal to be compared with a Mod distribution model that can be assigned to it (dotted line curve)
• FIG. an arithmetic coding (contextual for the coding of the plane P ⁇ -2 in the example shown) of bit planes whose probability tables have been calculated dynamically by the method in the sense of the invention
• FIG. flowchart of the bitmap coding with a contextual initialization of the probability tables according to the second embodiment mentioned above
• FIG. 14 presents the flowchart of the bitmap coding with a contextual initialization of the probability tables in the case where only two possible contexts are imposed, according to the third embodiment mentioned above.
• the present invention proposes a coding / decoding processing using symbol planes exploiting a probability distribution of the source to be encoded in order to estimate a priori the probability of the symbols (for example 0 and 1) for each plane.
• This treatment aims at an optimization of the entropy coding by bringing a dynamic knowledge of the tables of probability.
• contextual arithmetic coding can be considered as an example of entropy coding.
• An example is described below in which the coding in the sense of the invention is carried out without loss of the indices resulting from the quantization of the transform coefficients of the frequency coders, in particular for speech and / or audio signals. Nevertheless, the invention also applies to lossy coding, in particular of signals such as image or video signals.
• FIG. 5 illustrates an example of an encoder using a distribution model of the signal to be coded in order to know a priori the probabilities of the symbols 0 or 1 by bit planes, within the meaning of the invention.
• the structure of the encoder is very close to an encoder of the prior art described in the document Oger et al: "Transform audio coding with arithmetic-coded scalar quantization and model-based bit allocation ", M. Oger, S. Ragot and M. Antonini, ICASSP, April 2007.
• the encoder described in this document determines a signal distribution model for estimating a form factor ⁇ which in the cited document only serves for flow control purposes.
• this type of encoder leads a coding according to the so-called “stack-run” technique and which has nothing to do with a coding by bit planes within the meaning of the invention.
• the invention can advantageously take advantage of a pre-existing structure comprising a form factor calculating module 505 (FIG. 5) and furthermore use this module 505 to perform bit-plane coding as described below.
• the encoder in the example represented comprises: a high-pass filter 501, a perceptual filtering module 502, a LPC analysis module 501 (for Linear Prediction Coding) and quantization, to obtain the short-term prediction parameters, a 504 conversion module MDCT (for "Modified Discrete Cosine
• the module 505 for calculating a form factor ⁇ , from a generalized Gaussian model in the example described, a rate control module 506, in particular as a function of the number of bits used Nb, a module 507 which also uses the module 505 to carry out the calculations serving at least the initialization of the probability tables of the coding module 509 by bit planes, in a first embodiment, and, in other subsequent embodiments, the calculating contexts, a uniform scalar quantization module 508, the bitmap coding module 509, a noise level estimation and quantization module 510, - a multiplexer 511 of the outputs of the modules 503, 505, 509, and 510 for storing encoded data or transmission for subsequent decoding.
• a uniform scalar quantization module 508 the bitmap coding module 509
• a noise level estimation and quantization module 510 - a multiplexer 511 of the outputs of the modules 503, 505, 509, and 510 for storing encoded data or transmission for subsequent decoding
• the input signal x (n) is filtered by a high-pass filter (501) in order to remove the frequencies below 50 Hz. Then, a perceptual shaping filtering is applied to the signal (502) and in parallel an LPC analysis is further applied to the signal (503) filtered by the module 501.
• An MDCT analysis (504) is applied to the signal after perceptual filtering.
• the analysis used may for example be the same as that of the standard 3GPP AMR-WB + encoder.
• the form factor ⁇ is estimated on the coefficients of the MDCT transform (505). In particular, once the estimate of the form factor has been made, the quantization step q which is suitable to reach the desired rate (506) is calculated.
• the encoding is performed by transforming with a bitmap coding whose probability tables are initialized in real time, in the sense of the invention, according to an estimated distribution model. dynamically depending on the signal to be coded.
• the first part of the MDCT before conversion (modules 501 to 504) is equivalent to that used for the transform encoding with stack-run encoding presented in the document Oger et al cited above.
• the estimation of the form factor (module 505) as well as the flow control can also be common.
• the information of the determined model is used here to also estimate the probability tables (module 507) of the symbols 0 and 1 which will be used to initialize the coding module 509.
• scalar quantification is performed.
• module 508 the reference 512 representing a division module.
• the quantization can be, too, common to that described in the document Oger et al, but here it is followed by a bitmap coding (module 509) whose initialization of the probability tables is done, as indicated below. before, following a model (defined by module 505).
• An estimate of the noise level (module 510) is made which may still be common to that of the reference Oger et al.
• the parameters of the encoder are finally transmitted to the decoder via a multiplexer 511.
• a homologous decoder may comprise: a demultiplexing module 601 of the stream received from the coder of FIG. 5, a module 602 for decoding the LPC coefficients, a module 603 for estimating probabilities based on the model defined by the module 505 of FIG. 5, a module 606 for decoding the quantization step q, a noise level decoding module 605, using the value of the decoded quantization step, a bit plane decoding module 604 receiving the estimated probabilities (module 603) to deliver, by using the value of the decoded quantization step; , the decoded integer vector Y (k), a noise injection module 607,
• a de-emphasis module 608 for finding the decoded vector X (k), expressed in the transformed domain, a module 609 for the inverse MDCT transform, and a module 610 for inverse perceptual filtering from the decoded LPC coefficients. (module 602), to find a signal x (n) which, without loss or truncation in the communication, corresponds to the original signal x (n) of FIG.
• the number of bits Nb used by the coding is returned to the bit allocation module in order to modify (or adapt) the value of the quantization step, so that number of bits remains less than or equal to the available bit budget.
• the MDCT spectrum is therefore coded in a rate control loop with typically 10 to 20 iterations, to arrive at an optimal quantization step q opt .
• the initial quantization step fixed for the first iteration on the determination of the optimal quantization step q opt , is estimated from the form factor ⁇ that delivers the module 505 for determining a generalized Gaussian model.
• model-based coding consists of quantifying and encoding the source not directly, but from a probability model.
• A amplitude
• This signal X may for example be delivered by the module 504 of FIG. 5 and then correspond to a signal MDCT which is a function of the frequency (freq).
• the signal X is intended to be quantized by a quantization step q, to obtain (at the output of the module 508 of FIG. 5) the signal referenced Y and corresponding to a sequence of components y ,.
• the signs and absolute values a, of these components y, and these absolute values a are decomposed into sections of bits MSB ... LSB shown in FIG.
• This histogram H is then modeled by the model Mod (in dashed lines) which may for example be Gaussian.
• the distribution H of the signal X can finally be represented by a probability density model (reference pdf for "probability density function"), following a simple scale change of abscissa (of VaI ( X,) to Val ( ⁇ ,), the reference Val ( ⁇ ,) denoting the different possible values that can take each absolute value of component a,).
• FIG. 7 illustrates, by way of example, the density of probabilities of a generalized Gaussian, which is a particular model that can advantageously be chosen.
• f ⁇ a mathematical expression
• the probability density of a generalized Gaussian z source, of zero mean and of standard deviation ⁇ , is defined by: where ⁇ is the form factor describing the shape of the exponential function (FIG. 7), the parameters A ( ⁇ ) and B ( ⁇ ) being defined by:
• the source (the signal to be coded) is modeled as the result of a random draw of a generalized Gaussian variable.
• This generalized Gaussian model can then advantageously be used to model the spectrum to be coded in the field of the modified discrete cosine transform (MDCT). From this model, we can derive the value of the form factor ⁇ that characterizes the model. It is recalled that advantageously, the form factor ⁇ is already estimated for each signal block (or frame) from the spectrum to be coded, in some existing encoders which integrate a module such as the module 505 of FIG. the quantization step q.
• the estimation of the distribution model (which can lead in particular to the form factor ⁇ ) also makes it possible to calculate the probabilities of the symbol values per planes. This technique is described below.
• the estimation of a probability p ( ⁇ ,) of having a value of component a, among N possible values is based on the following calculation:
• Figure 7 also illustrates the different intervals for calculating the probability p ( ⁇ /).
• the calculation of the probabilities p ( ⁇ j can be carried out by conventional integration methods.
• the trapezoidal method which is simple to implement, is preferably used in a preferred embodiment and the value of the difference is preferably standardized.
• -type ⁇ to 1 so that the quantization step, for the computation of the integral in the equation above, becomes q / ⁇
• This operation allows a more efficient computation of the integrals, because one thus removes the problem of the variation of dynamics on the signal and is reduced to a centered source of unit variance whatever the value of the form factor.
• an estimate of the probability of having bits at O or 1 for each bit plane Pk is provided, thereby defining what was referred to above as the initial tables of probabilities. These tables will be described with reference to Figure 12 discussed below.
• conditional probabilities of O or 1 as a function of the already coded bits and at the same position in previous planes (these bits then defining a context).
• an estimate of the conditional probabilities is provided as a function of a number of possible context values limited to two ("significant or non-significant" context).
• the probability of 0 and 1 in each plane can take a value which can, in practice, be very different from 1/2 and, more generally, be very different from one signal frame to another, for example according to the degree of voicing of the signal as will be seen later.
• the flow diagram of FIG. 8 presents the principle of bitmap coding with, according to the first embodiment, an initialization of the probability tables, for each plan Pk, which is based on a model.
• the model parameters which are the form factor ⁇ and the standard deviation ⁇ are first estimated (step 801 after the start step 800).
• the value of the scalar quantization step q (step 802) is then determined, for example from that of the factor ⁇ as represented in FIG. 5. From the parameters ⁇ , ⁇ and q, the probabilities of the components a are estimated. , (step 803) as previously described. According to a principle similar to that described above with reference to FIG.
• step 808 it is checked whether there remain bit planes to code using the test 805 on the current value of a decremented loop index k (step 808) from KI to 0. It is then estimated the probabilities of having a bit at 0 or 1 in each plane (step 806) and then the coding of this plane (step 807) is performed using this information on the probabilities. This loop is carried out as long as the index k is positive or zero (as long as there are plans to be coded). Otherwise, the processing terminates (end step 809) or can be implemented again for a next block of signal (or frame) to be encoded.
• step 901 the parameters ⁇ , ⁇ and q (step 901) characterizing the distribution model are decoded which was used in coding.
• the probabilities associated with the components a, (step 902) are then estimated with this model.
• a loop is then applied with a decrement (step 907) of the loop current index k initially set to KI (step 903).
• the probabilities of 0 and 1 in each plane Pk (step 906) are estimated in order to also decode each plane P.sub.k (step 907) more efficiently. If ⁇ k less than or equal to 0 corresponding to the output N of the test 904), no more plan is to be coded and the processing can be terminated (end step 908) or implemented again for a next block ( or frame) to be decoded.
• the probability of obtaining the value 0 in a plane Pk can be calculated from the probability model still corresponding to a generalized Gaussian model in the example described.
• b k and M are respectively: a random variable representing any bit in the plane P k .
• bitmap coding technique itself, remains substantially unchanged from the prior art.
• the amplitude of the signal MDCT is strong (in absolute value) on only a few frequencies which follow each other (the significant bits having a value of 1 for these frequencies), while the amplitude associated with the other frequencies is relatively low (the significant bits keeping a value at 0).
• the MSB plane and the immediately following plane (s) have few bits to 1.
• the LSB plane of the least significant bits and the planes which immediately precede it can comprise, according to a very schematic explanation, as many 0s as of 1, according to the fluctuations of the noise, and the probability of finding there values of bits at 0 is then average (close to 0.5).
• the calculations of the probabilities are carried out directly on the signal, in real time, preferably by an a priori estimation of the signal distribution model (module 507 of FIG. 5 and 603 of FIG. 6) as described above.
• FIG. 13 presents the principle of bitmap coding with context determination for each bit of a Pk plane, in a second embodiment of the invention. Elements similar to those in the flowchart of Figure 8 have the same references and are not described again here.
• the probabilities associated with the different possible values of context for each plane are estimated (step 1306).
• the term "context” means, for the ith bit of the k th plane, the set of bits of rank i in the planes preceding the plane Pk.
• the context is "1" (value of the bit of rank 7 in the plane P 2 (MSB))
• the context is "11” (where 1 is the value of the rank 7 bit in the P 2 plane (MSB) and 1 is the value of the rank 7 bit in the Pi plane).
• the probabilities are then estimated as a function of the context found (step 1307) for the rank of this bit.
• This treatment is reiterated for a next plane, taking into account the context for each bit.
• This loop is carried out as long as there are plans to be coded (arrow O at the output of test 805). Otherwise (arrow N at the output of test 805), the coding is completed or can be implemented for a next signal block (or frame).
• the number of possible contexts is 2 ⁇ "k .
• the different possible values Ck.n of the contexts on the plane Pk are defined as follows:
• this maximum number is two and is thus interpreted: a context at 0 indicates that the bits coded in the higher planes and at the same rank are all equal to 0 and therefore the quantified MDCT coefficient, for this reason. rank, is for the moment insignificant, and a context at 1 indicates that at least one of the bits already coded in the higher planes and at the same rank was equal to 1, which implies that the current coefficient, for this rank, is significant.
• the flowchart of FIG. 14 presents the principle of bitmap coding with a context determination for each bit of a Pk plane, limiting the number of possible contexts to two ("0" or "1" to step 1406). The elements similar to those of the flowcharts of FIGS. 8 and 13 bear the same references and are not described again here. Only steps 1406, 1407 and 1408 are modified in the sense that the only possible values of the context are now 0 or 1, which also influences the coding performed (step 1408).
• conditional probability of having the value zero, for k ⁇ K1 is conducted by exploiting the knowledge of the context (presence of an equal bit to 1 in the planes of rank k + 1 to KI) during the coding of the plane of rank Pk.
• conditional probability for k ⁇ K-1 is defined as follows:
• Ck is a random variable representing the context associated with any bit bk in the plane Pk.
• the invention leads to an efficient bitmap coding technique and makes this type of coding more flexible than in the state of the art sense. . Indeed, it becomes possible to no longer store pre-calculated probability tables (contexts). A dynamic calculation, based simply on the signal to be coded / decoded, then suffices.
• the present invention also aims at an encoder for implementing the method of the invention, such as that represented by way of example in FIG. 5 described above, and then comprising a module 505 for estimating a distribution of the signal. to code, feeding a module 507 for calculating the probabilities of symbol values. It also relates to a decoder for implementing the method of the invention, such as that represented by way of example in FIG. 6 described above, and then comprising a module 603 for calculating the probabilities of symbol values, starting from an estimate of a signal distribution. In particular, this module 603 is powered by at least one parameter (for example the form factor ⁇ ) characterizing the probability density model of the signal before coding, this parameter ⁇ being received by the decoder in coded form and then being decoded ( reference of Figure 6).
• a parameter for example the form factor ⁇
• the present invention also relates to a computer program intended to be stored in a memory of such an encoder or such a decoder. It includes instructions for implementing the method of the invention, when it is executed by a processor of the encoder or the decoder.
• a computer program intended to be stored in a memory of such an encoder or such a decoder. It includes instructions for implementing the method of the invention, when it is executed by a processor of the encoder or the decoder.
• the flow charts of FIGS. 8, 9, 13 or 14 can schematize respective algorithms of different versions of such a computer program.
• the principle of the invention could also be applied to the case of a stack-run coding where the probabilities of four symbols (0,1, +, -) for "stacks" and "runs "are calculated from a distribution model of the signal to be coded (according to the reference Oger et al previously given), for example from a generalized Gaussian model.
• a distribution model of the signal to be coded for example from a generalized Gaussian model.
• the invention makes it possible to optimize the contexts of the contextual arithmetic coding.
• the coding in the sense of the invention may be contextual arithmetic
• the coding may also be adaptive (for example as a function of the bit rate, the source, or the values taken by the bits of the same plane) as described for example in the reference Langdon et al cited above.
• the invention applies to any type of coding (Huffman, or others) based on the probabilities of symbols in symbol plane coding.
• the invention can be applied more generally to other types of entropy coding than arithmetic coding.
• models other than the generalized Gaussian model are possible.
• models of fixed probabilities a Laplacian model in particular
• parametric models alpha-stable models, Gaussian mixing models, or others

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