EP2183851A1

EP2183851A1 - Encoding/decoding by symbol planes with dynamic calculation of probability tables

Info

Publication number: EP2183851A1
Application number: EP08828177A
Authority: EP
Inventors: Marie Oger; Thi Minh Nguyet Hoang; Stéphane RAGOT; Marc Antonini
Original assignee: France Telecom SA
Current assignee: Orange SA
Priority date: 2007-08-24
Filing date: 2008-07-25
Publication date: 2010-05-12
Also published as: US20110116542A1; JP2010537533A; JP4981174B2; CN101842988B; CN101842988A; WO2009027606A1

Abstract

The invention relates to an arithmetic encoding by bit planes (MSB,..., LSB), that comprises using tables of probability to have a 0 or 1 bit for encoding each bit plane. According to the invention, the probability tables are calculated dynamically for each signal frame based on a probability density model (Mod) corresponding to the distribution (H) of the signal (X) on each frame.

Description

Encoding / decoding by symbol planes, with dynamic calculation of probability tables

Field of the Invention 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.

Prior art

Among the basic methods of compressing digital signals are lossless compression methods (Huffman coding, Golomb-Rice coding, arithmetic coding), also referred to as "entropy coding", compression methods, lossy, resting on a scalar or vector quantization.

With reference to FIG. 1, a compression encoder, general, 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.

In the following, the analysis and the synthesis are not discussed. Only quantization is considered, followed by the associated coding and / or decoding. We are particularly interested here in the scalar quantization of a data block followed by coding, by symbol planes, quantization indices. This coding technique, used in several signal compression standards (in audio coding MPEG-4 in the coder "Bit Sliced Arithmetic Coding" (or BSAC), in encoding JBIG images on the bit planes of an image, encoded in particular according to the JPEG2000 standard, in MPEG-4 video coding), is schematically in Figure 2.

With reference to FIG. 2, the scalar quantization followed by coding by symbol planes typically involves, at coding: an adaptation module 200 of the source signal S for delivering a vector denoted by X = [X ₁ • • • x _N ] of dimension N ≥ \, a scalar quantization module 201 delivering a quantized vector defining a sequence of integer values Y = Iy ₁ • • • y _N ],

a symbol plane decomposition module 202 which may be bits at 0 or 1, this module 202 then delivering a vector of values P _k = [a _lk - - - U _{7V 4} ] with k = 0, - - - , K - l, and a sign vector S = [s _ι ^{• • •} %],

a module 203 for performing the coding by bit planes and a multiplexing of the coded values, and a rate regulation module 204, according to the number of bits Nb to be used for the transmission; and, at decoding:

a demultiplexing and decoding module 206, and an integer conversion module 207 for delivering a vector Y such that Y = Y, in the absence of bit errors and without truncation of the bitstream.

Reference 205 illustrates the transmission channel from the encoder to the decoder, which may optionally apply truncation of the bit stream.

Thus, starting from the adapted signal, to be coded, X = [X ₁ • • • x _N ], the scalar quantization

(conducted by the module 201) produces a sequence of integer values Y = Iy ₁ • • • y _N ]. The decomposition in bit planes (carried out by the module 202) first returns to separate signs and absolute values, as follows: then to decompose the absolute values in binary form, with: α _! = B _κ.1 (α _! ) 2 ^κ - ¹ + - B _k (α _! ) ^2k + ... + B ₁ (α _! ) 2 ¹ + B ₀ (α _! ) 2 °, where:

B _k ((Z ₁ ) is the k ^th bit of the binary decomposition of the absolute value a, the quantized component Y ₁ , and

K is the total number of bit planes for the decomposition of the set of values at _t , this number K being defined by: where [.] is the rounding to the upper integer and with Iog ₂ (θ) = -∞. Note that the sign of the zero value being undefined, the above convention (S ₁ = O for y _t = 0) can be changed (in ^ = I for y _t = 0).

The entropic coding of the planes (module 203) can advantageously be achieved by a so-called "contextual arithmetic" coder. The principle of an arithmetic coder is explained in Witten et al:

"Arithmetic Coding for Data Compression", LH. Witten, R.M. Neal, J.G. Cleary,

Communications of the ACM - Computing Practices, Vol. 30, No. 6 (June 1987), p.520-540.

It will be noted, for example with reference to Table I (page 521) of this Witten et al. Document, that probability tables must be set initially to carry out the coding. In a so-called "contextual" arithmetic coder, the data that are drawn from the probability tables for the symbols 0 and 1 are not always the same and can evolve according to a context that depends, for example, on the values of the bits already decoded at the time. around (for example, in higher bit planes and in adjacent elements). The principle of a contextual arithmetic coder is described in particular in the document Howard et al: "Arithmetic Coding for Data Compression", PG Howard and JS Vitter, Proc. IEEE, vol. 82, no. 6 (June 1994).

In general, 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 bits of sign S ₁ , for i = \, - - -, n, are transmitted only if the corresponding absolute value α _; is non-zero. To allow partial decoding of the bit planes, the sign bit S ₁ is transmitted as soon as one of the decoded bits {α _α } _{i = 0 κ} _ _γ equals 1.

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.

At decoding, 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. In the absence of binary errors and without truncation of bitstream, we have of course:

P _k = P _k , S = S and thus Y = Y

In the rest of the document, for the sake of clarity, it is assumed that there are no binary errors.

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. An example of bit plane decomposition is given in Figure 3 for N = S. In the example shown, the vector Y is such that Y = [-2, +7, +3.0, + 1, -3, -6, +5]. The non-zero values {y _t } _{ι = ι N} are said to be "significant" (reference VS in FIG. 3). The sign bits are represented by the vector bearing the reference sgn in FIG. 3. In this case, we have 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] and S = [1,0,0, 0,0,1,1,0].

The vector P _k then represents a plane of bits of weight k. The upper bit plane

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).

We will now describe, in more detail, the operation of the module 203 of FIG. 2, with reference to FIG. 4 corresponding to a flowchart of the arithmetic coding by bit planes (following a scalar quantization). This is a coding with multiplexing of dimension N in the sense of the state of the art. After a start step 400, the total number K of bit planes (step 401) is obtained. A current loop index k is decremented and the value of this current index is initially set at k = K1 (step 402) to end the treatment at k = 0. The test 403 verifies that the value of k = 0 has not yet been reached. As long as this value k = 0 is not reached (arrow O), the plane Pk of current index k (step 404) is coded. The first loop for which k = Kl thus deals with the plane Pκ-i corresponding to the plane MSB and the last loop for which k = 0 treats the plane Po corresponding to the plane LSB. At step 405, the signs of the new significant coefficients associated with the plane Pk are transmitted. The next step 406 aims to decrement the value of the current index k. If the plane Po for the value of k = 0 has been processed (arrow N at the output of the test 403), the processing is finished (end step 407) or starts again for a new block of data of the signal (or frame). 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. Indeed, 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. The adaptive arithmetic coder is thus reinitialized as soon as we begin to code a new plane P _k , in particular by initializing the probabilities of 0 and of 1 to a value of 1/2 (= 0.5) and, as and when as the same plan is coded, these probabilities evolve and are adapted by updating the frequency of 0 and 1. A detailed description of this type of encoding is given in particular in the document:

"An introduction to arithmetic coding", G.C. Langdon, IBM J. Res. Dev. 28, 2, p.135-149 (March 1984).

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

(then having predefined frequency values). More generally, 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.

Presentation of the invention

It proposes for this purpose a method of processing a signal for coding / decoding in compression of the signal by symbol planes, in which probabilities of symbol values are determined for at least one plane.

For the purposes of the invention, these probabilities are calculated dynamically from an estimate of a distribution of the signal.

Preferably, the signal being quantized before the coding, 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).

In a first embodiment, 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.

In a second embodiment, 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.

More particularly, for the same signal value position in said succession of 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. In a third embodiment, a limited number of possible values of the context is chosen, preferably a number of two, with:

a first context value designating the occurrence of at least one significant symbol value in the planes representing more significant symbol values,

a second context value signifying that no significant symbol value occurrence has been found in the planes representing more significant symbol values.

Thus, 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.

One can, indeed, "use" a model of the source to be coded because some coders / decoders already implement such a modeling, in particular to calculate the form factor (usually noted α) of the signal to be encoded. We can then rely on a pre-existing signal distribution model, for example used for calculating the form factor α in the transform encoder with stack-run coding and presented in the document Oger et al:

"Transform audio coding with arithmetic-coded scale quantization and model-based bit allocation", M. Oger, S. Ragot and M. Antonini, ICASSP, April 2007. However, it is stated here that this document does not disclose any coding by symbol plans. List of Figures

Other features and advantages of the invention will emerge on examining the detailed description below, and the appended drawings in which, in addition to FIGS. 1 to 4 described above: 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 (α,), - 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. 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 _κ-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, and 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. detailed description

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.

The case of 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, as represented by way of example in FIG. 5, 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. In particular, the encoder described in this document determines a signal distribution model for estimating a form factor α which in the cited document only serves for flow control purposes. Moreover, 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.

Nevertheless, 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. With reference to FIG. 5, 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

Transform ") and frequency shaping,

the module 505 for calculating a form factor α, 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.

Thus, 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 α 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. Then, a uniform scalar quantization of the signal following this quantization step (507), the module 512 of Figure 5 making a division by this step. Thus, a sequence of integers Y (k) is recovered which are then coded by the module 509. An estimation of the level of noise to be injected at the decoder (module 510) is also preferentially carried out.

Thus, in the example shown in FIG. 5, 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. On the other hand, 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. Next, scalar quantification is performed. uniform (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.

Referring now to FIG. 6, 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.

It is also indicated, with reference again to FIG. 5, that 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 . More particularly, 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 α that delivers the module 505 for determining a generalized Gaussian model.

The operation of this module 505 is described below.

Unlike conventional coding, the so-called "model-based" (probabilistic) coding consists of quantifying and encoding the source not directly, but from a probability model. Referring to Figure 11, there is shown the variation of the amplitude (A (MDCT)) of a signal to be quantized and coded (referenced X and therefore corresponding to a sequence of components X ₁ ). 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). Recall that 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.

More particularly, to obtain the histogram H corresponding to the distribution of the signal X (right graph in FIG. 11): one "counts" all the occurrences where the components x, of the signal X are equal to 0 and the number is postponed obtained on the ordinate (Hist) of the graph, on the abscissa 0, then we count all the occurrences they are equal to 1 and we report the number obtained on the ordinate, on the abscissa 1, and so on for the following values 2 , 3, etc., and -1, -2, -3, etc. Consequently, the reference Val (x,) in FIG. 11 (abscissa of the graph on the right) indicates all the possible values that the signal X can take.

This histogram H is then modeled by the model Mod (in dashed lines) which may for example be Gaussian. Referring now to FIG. 7, 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 (α,), the reference Val (α,) 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. We give a mathematical expression (noted f _α ) below.

The probability density of a generalized Gaussian z source, of zero mean and of standard deviation σ, is defined by: where α is the form factor describing the shape of the exponential function (FIG. 7), the parameters A (α) and B (α) being defined by:

. . ccB (α, vr (3 / α) A (α) = - Γ - ^ - and B (α) =, 'y' 2r (1 / α) ^V; \ r (l / α) where F is the function Gamma defined as follows: r (α) = { _o V t ^"+1 dt

Thus, 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 α that characterizes the model. It is recalled that advantageously, the form factor α 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.

For the purposes of the invention, the estimation of the distribution model (which can lead in particular to the form factor α) also makes it possible to calculate the probabilities of the symbol values per planes. This technique is described below. With reference again to FIG. 7, the estimation of a probability p (α,) of having a value of component a, among N possible values (referenced VaI (λ) in FIG. 7) is based on the following calculation: Figure 7 also illustrates the different intervals for calculating the probability p (α /). We already observed that the generalized Gaussian distribution is symmetrical, we have p ^(α J ⁼ p ( ^"α J - We will also report that the intervals are regular because it implements a uniform scalar quantization step q (for the components y , (or a,) from the components X ₁ ) It will also be noted that the higher the maximum value of the components a, the greater the associated probability p (α,) is low.

The calculation of the probabilities p (αj 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 σ to 1 so that the quantization step, for the computation of the integral in the equation above, becomes q / σ 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.

Three embodiments are presented below to estimate the probabilities of the symbols O and 1 by bit planes from these probability calculations p (α,).

In a first embodiment, 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.

In a second embodiment, provision is made for estimating 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). In a third embodiment, 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).

It is recalled that, in the state of the art, the probabilities of 0 and 1 initially in a plane Pk were set to 1/2 = 0.5, or at best were prerecorded in a table. Now, 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 α and the standard deviation σ 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 α as represented in FIG. 5. From the parameters σ, α 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. 4, 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.

Referring now to FIG. 9, at decoding, after a start step 900, the parameters α, σ 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). As long as the index k is positive (arrow O at the output of the test 904), 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.

We saw above how are computed the probabilities associated with the values of components a ,. It will now be described how, for each plane P _k , it is possible to calculate the probabilities associated with a given symbol (step 806 of FIG. 8 and 905 of FIG. 9). In order to simplify the notations in the equations, the probability p (α,) associated with a component a, is denoted by "p (α)" below.

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. The probability of having the k ^th bit of the binary decomposition of a component a, (thus in the plane Pk), equal to zero, is given by: l if x ⁼ y, which is noted below yp (B _k (α) = 0) for convenience in writing equations.

The relation that makes it possible to have the probability of having the symbol 0 in the plane Pk is

,, p (b _k = 0, α ≤ M) then given by: p (b _k = 0 | a ≤ M) =,

where b _k and M are respectively: a random variable representing any bit in the plane P _k , and

- the largest integer in absolute value that we can have on K planes, M = 2 ^K -1. It will be noted that the expression of the probability is dependent on the total number of planes K and thus on the number of integers that can be encoded. Indeed, it is assumed here that the number of coded planes is written in the bit stream and this data is therefore available for decoding and coding, in particular before the arithmetic coding of the plans Pk. We therefore have a so-called "conditional" probability: knowing that a ≤ M.

M

The probability p (α ≤ M) is defined by: p (a ≤ M) = V p (α). α = -M

M

The probability p (b _k = 0, a ≤ M) is defined by: p (b _k = 0, a ≤ M) = J ^ PΦ _k ( ^α ) ⁼ 0) • α = -M

To simplify the writing of the equations, we note below the value p (b _k = 0 | a _t ≤ M) (or p (b _k = 0 1 a ≤ M)) as follows: "p _M (b _k = 0) ". We then obtain the following expression of the probability of having the value 0 in a plane P _k (step 806):

1 M 1 M

P _M (K = O) = - x £ p (B _k (α) = 0) = - x £ p (α) xδ _{Bk (fl) o}

P p ( ^β ) ^a - ⁼ - ^M p p ( ^β ) ^{M M} a = -M a = -M

It will be noted that the probability p (α,) (or p (α)) occurs in this last equation, which justifies its calculation prior to steps 803 and 902 of FIGS. 8 and 9.

The bitmap coding technique, itself, remains substantially unchanged from the prior art. The essential difference, however, is the initialization of the probabilities of 0 to the value p (B _k (α) = θ) given above, instead of choosing by default an initialization value of 1/2 or a value prerecorded initialization depending on the flow rate or the source.

Moreover, in order to obtain the probability of having the value 1 be p _M (b _k = 1), we simply use a complementarity relation of the type: p _M (b _k = 1) + p _M (b _k = 0) = 1. Figure 10 shows an example of the different values {a, = 0, 1, 2, 3, ..., 7) that can be taken on K = 3 planes. Thus, for the plane P ₂ (MSB), the bits whose value is zero correspond to the integers 0, 1, 2 and 3 (solid line) and therefore the probability of having the value 0 on the MSB plane is given, in taking the last equation above, by: p _M (b ₂ = 0) = p (α _i = 0) + p (α _i = 1) + p (α _i = 2) + p (α _i = 3)

In the same way, for the plane Pi, the bits at the value zero correspond to the integers 0, 1, 4 and 5 and: p _M (b ₁ = 0) = p (α _! = 0) + p (α, = l) + p (α, = 4) + p (α, = 5), and so on.

We now explain, returning to Figure 11, what the result of these probability calculations represents. In this figure, there is shown purely by way of illustration a spectral signal X which has the distinction of being very harmonic (or "tonal").

Thus, 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). As a result, the MSB plane and the immediately following plane (s) have few bits to 1. With the pace of this signal, a small value of the shape factor α (less than 0.5) can be found and the probability of 0 bit values are high (close to 1) for the MSB plane and those immediately following it. On the other hand, 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).

It should be noted that if the signal was less harmonic and more noisy (for example an unvoiced speech signal), the probability of finding bit values at 0 in the plane

MSB would be lower (closer to 0.5). This observation is detailed in the reference Oger et al (Figure 1 and its comments). Thus, if the signal of FIG. 11 is brought back in the form of a histogram as described in this reference Oger et al, a narrow peak (reference H of FIG. 11) is obtained, with a small width value at half height (giving the form factor α). On the other hand, for a signal strongly noisy or unvoiced, the histogram would have a larger peak and a larger α-form factor. It will be understood here how the Mod distribution model of the source to be encoded (approximating the histogram H of FIG. 11) is linked, on the one hand, and the probabilities of the bit values at least in the first plane MSB, of somewhere else.

These calculated probability values can then be given to an arithmetic coder (or to an arithmetic decoder), for example such as that described in the reference Witten et al cited above: "Arithmetic Coding for Data Compression", LH. Witten, R. M. Neal, J. G. Cleary, Communications of the ACM - Computing Practices, Vol. 30, No. 6 (June 1987), p.520-540.

In this case, with reference to FIG. 12 (which can be compared with FIG. 1b (page 522) of this document Witten et al), the statements p _M (b _κ.j = 0) = A and p _M (b _κ.j = l) = B define the probability tables of the Pκ-i plane (MSB) (which can be compared with table I (page 521) of this document Witten et al).

Thus, it is possible, by the implementation of the present invention, to calculate, on a frame-by-frame basis, the probability tables p _M (b _κ- ₁ = 0), p _M (b _κ- ₁ = 1) at least for the MSB plane, directly from the actual form of the signal and without having recourse to a pre-registration of probability tables as in the sense of the prior art, thus requiring additional memory resources, both encoder and decoder, and limiting the flexibility of implementation. For the purposes of the invention, 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.

The calculation of the values A = p _M (b _κ.1 = 0) and B = p _M (b _κ.1 = 1) corresponds to what has been designated above by the terms "initialization of the probability tables". This operation is preferably performed for each plane. In the above-mentioned first embodiment, these probabilities are calculated for a current plane Pk without taking into account bit values in planes other than Pk. In a second embodiment, these values are taken into account by defining a "context".

In fact, with reference to FIG. 11a new, it can be seen that in the planes immediately following the MSB plane, if a bit of a plane was at 1, the bit of the same rank in the immediately following plane is very frequently also at 1. Of course, Figure 11 is presented for illustrative purposes only but this observation can be carried out in practice on real cases. Typically, if a bit of a rank i is 1 in a plane, then it is "more likely" that the bit of the same rank is also 1 in a subsequent plane. Conversely, it is usual for the amplitudes associated with a few frequencies in a signal spectrum to be almost zero (especially in the case of a speech signal). Thus, if the bit of a higher plane Pk is zero, it is "more probable" that a bit of the same rank in the following plane P _k -i is also zero. Therefore, to estimate the probability associated with a bit in a plane, it is advantageous to take into account the value of the bit of the same rank in a previous plane. This observation can be exploited by defining, from a value observed for a bit of rank i on a plane P _k (for example the only bit at 1 of the MSB plane of FIG. 11), a context for a bit of the same rank i and on the plane P _k -i following (bit also 1 in this plane).

The exploitation of this principle in particular is carried out by the so-called "contextual" arithmetic coders in the embodiments described below.

They implement a model-based bit plane encoding allowing conditional probability computation for Pk planes with k <K1. The bitmap coding processes described above did not exploit mutual information between planes Pk, since the planes Pk were coded one by one and independently of one another. We are now presenting a way of exploiting already coded information. The bit plane MSB is encoded as in the previous case, independently of the other bit planes by initializing the probability of 0 and 1 from the generalized Gaussian model. On the other hand, the coding of the plane Pk for k <K1 here uses the knowledge of a "context" information on the previous plans P _κ.15 ..., P _{k + 2} , P _{k + 1} •

Overall, we compute probability tables for different possible contexts, so for different possible bit values taken in previous plans.

For example, with reference to FIG. 12 again, for the plane P _K-2 , two probability tables (each table for a bit of the plane P _κ- 2 will be equal to 0 or 1) will be computed. according to the possible bit values in the preceding plane P _κ- i (a table for a value at 0 and a table for a value at 1), and therefore according to the context noted C in FIG. 12. In the example shown, the value of the bit of rank z ^' = 0 in the plane Pκ-i was 0, so the context is worth C = O and the associated table of probabilities is given by the values A' and B '. For the rank i = \, the value of the corresponding bit in the plane Pκ-i was 1, so the context is worth C = I and the associated probability table is now given by the values C and D '. For the rank i = 2, the value of the corresponding bit in the plane Pκ-i was 0, so the context is worth C = O and we take again the table of probabilities given by the values A 'and B'. Recall that the rank i designates the index i of a component a, or y ,. It will be noted in FIG. 12 that the contexts C of the MSB plane are not defined (because, of course, there is no more significant bit plan). For a computer implementation of this realization, we will then set the contexts of the MSB plane as being all equal to 0.

We do not detail here how the planes are coded, nor how are the intervals of probabilities successively divided (even if the limits of the intervals are indicated in FIG. 12). We can usefully refer to the Witten et al document for the description of such elements. The flowchart of 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.

If at least one plane is to be coded (arrow O at the output of the test 805), the probabilities associated with the different possible values of context for each plane are estimated (step 1306). In the second embodiment, 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. Thus, with reference to FIG. 10, for rank 7, in the plane P ₁ , the context is "1" (value of the bit of rank 7 in the plane P ₂ (MSB)), while in the plane Po, 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 context being thus defined for a current bit, the probabilities are then estimated as a function of the context found (step 1307) for the rank of this bit. We then code, with the probabilities thus calculated, each bit of a plane (step 1308 of FIG. 13) until the ranks are exhausted. 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).

Thus, at first, we compute the probability tables for different possible contexts, then we estimate the probability of having the value zero or the value 1 knowing the context, for each bit. The manner of calculating the probability tables for different possible contexts is described below (the values A ', B', C, D 'in the example of FIG. 12). The calculation of the probability of the contexts themselves C _k (α) (step 1306) is as follows. For the bit planes of rank lower than KI (other than the MSB plane), the contexts C _k (α) are defined as being the quotient of a, by 2 ^{κ ~ k} in the plane Pk, ie:

K-I

^C _k ( ^α ) = Σ B _j (α) 2 ^J , with -M ≤ α <M and for all k <K j = k + l For the plane Pk, the number of possible contexts is 2 ^{κ "k} . The different possible values Ck.n of the contexts on the plane Pk are defined as follows:

KI cκ _n = Σ ^B _j ( ⁿ ) ^2J - ^with 0 <n <2 ^{κ "k} and for all k <K j = k + l

Thus, in the second embodiment, with reference to the example of FIG. 10 where K = 3 planes, on the plane k = 1, there are four different contexts which are {00,01,10,1 1} and the probability of the ^kth context of a in the plane Pk equal to Ck, _n is given (in step 1306 of Figure 13) by:

P (C _k (α) = c, J = p (B _{k + 1} (α) = B _{k + 1} (n)) xp (C _{k + 1} (α) = H p (B _j Ia) = B ^ not))

Now, the computation of the conditional probability of having the value zero knowing the context C _k (α), for k <K1, is carried out, at the step 1307 of FIG. 13, as follows.

We try to exploit the knowledge a priori of the context (planes of rank k + 1 to KI) during the coding of the plane Pk. The conditional probability of having the value 0, knowing the context ct, n, for k <KI, is defined by: The following relations make it possible to determine the set of probabilities involved, for the 2 ^{κ ~ k} different possible context values (0, 1, 00, 01, 10, 11, 000, etc.):

The probability p _M (c _k = c _kn ), for k <K-1, is defined by the relation:

The probability p _M (b _k = 0, c _k = c _kn ), for k <K-1, is defined by the relation:

Thus, the conditional probability of having the value 0 knowing the context Ck, _n (step 1307), denoted p _M fb _k = 0c _k = c _Kn ), for k <KI, is finally defined by the relation:

An example of calculating the conditional probability for k <K1 is still presented in FIG. 10, in which, for the plane P ₂ (MSB), it is decided that all the contexts are null. For the plane Pi, there are two possible contexts 0 or 1, whereas for the plane P ₀ (LSB), there are four possible contexts that are {00, 01, 10, 11} and for the plane Po, the integers whose context is "00" are 0 and 1. The probability of having the context "00" (dashed lines of Figure 10) is therefore given by: p _M (c ₀ = 00) = p (α _! = 0 ) + p (α _! = l) In the case where the context is "00", the only integer whose bit in the plane Po has the binary value 0 is the integer 0. Thus, the probability of having a bit equal to zero in the plane Po, knowing that the context is "00", is given by:

Conversely, the probability of having a bit equal to 1 in the plane Po, knowing that the context is "00", is given by:

p _M (b ₀ = l | c ₀ = 00) = l -p _M (b ₀ = 0 | c ₀ = 00) = 1 - Pk = O)

P (U ₁ = O) HP ₁ = I)

Nevertheless, we note that the calculation of the probability tables for the last plans (including the LSB plan with 2 ^K possible contexts) is tedious given the exponential growth of the number of contexts to be taken into account. We now describe the third embodiment corresponding to a model-based bit plane contextual arithmetic coding, with calculation of the conditional probability for k <K1, in particular in the case where a limited number of possible contexts is imposed (here two possible contexts). It is a variant of the previous case corresponding to a conditional probability with contexts, in which, instead of having a number of contexts that increases by a factor of 2 to each new plan, as and when as we go down from the MSB plane to the plane

LSB, on the contrary we set a maximum number of contexts associated with a single bit (0 or 1).

In the example described, 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).

An example of calculation of the conditional probability, for k <K1, conducted at step 1406 of FIG. 14 with these two possible context values is presented below. With reference to FIG. 10, this example is repeated where the two possible contexts are 0 and 1. On the plane P ₁ , the bits whose context is "0" (which corresponds to having the value 0 on all the planes before the current plane, so on P ₂ corresponding to the plane MSB) are those of the integers Ci ₁ = 0, 1, 2 and 3. The probability of having a context equal to zero is then given by:

P _M (C, = 0) = p (α, = 0) + p (α, = 1) + p (α, = 2) + p (α _! = 3).

On the Po (LSB) plane, the bits whose context is "0" (referring to the planes Pi and P ₂ ) are those of the integers a, = 0 and 1. The probability of having a context equal to zero is then p _M (c ₀ = 0) = p (α, = 0) + p (α, = 1).

The calculation of the probability of having the context equal to 0 (step 1406 of FIG. 14) is carried out as follows. For the planes Pk with k <K-1 (other than the MSB plane), we define contexts:

. fl if there exists B. (α) = 1 for j = k + l, ... K-I

^C k ( ^α ) = 1

[0 otherwise

The probability of having the k ^th context of a in the plane Pk equal to zero is then given (step 1406) by a recursive relation of the form: p (C _k (α) = O) = p (B _{k + 1} (α) = θ) xp (C _{k + 1} (α) = O) =

The calculation of the conditional probability of having the value zero, for k <K1, with two possible context choices (at step 1407 of FIG. 14) 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. We then define the conditional probability for k <K-1 (step 1407) as follows:

where Ck is a random variable representing the context associated with any bit bk in the plane Pk.

The probability p _M (c _k = 0), for k <K-1, is given by the relation:

The probability p (b _k = 0, c _k = 0), for k <K-1, is defined by the relation

MM

P _M (b _k = 0, c _k = 0) = - -X

M £ [p (B _k (α) = 0) xp (C _k (α) = 0)]

Σ V (fl) a, = - M a = -M

So we have the conditional probability for k <Kl which is therefore defined by: P _M (b _k = 0 | c _k = 0) =

It is indicated that it is also possible to calculate p _M (b _k = 0c _k = 1) in a similar way.

The invention, according to any one of the three embodiments above, then 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 α) characterizing the probability density model of the signal before coding, this parameter α being received by the decoder in coded form and then being decoded ( reference of Figure 6).

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. For example, the flow charts of FIGS. 8, 9, 13 or 14 can schematize respective algorithms of different versions of such a computer program.

Of course, the present invention is not limited to the embodiments described above; it extends to other variants.

For example, arithmetic coders do not work, in practice, directly with the probabilities of symbols, but rather with the integer frequencies of symbols. The invention described above nevertheless adapts easily to the use of frequencies, since the frequencies correspond to the probability multiplied by a number of observed occurrences. We can still refer to the document Witten et al for more details on this point. It is therefore sufficient to convert the probabilities estimated above into frequencies.

More generally still, there are described above symbol planes whose values are "0" or "1" bit values. The invention nevertheless extends to an application to coding / decoding by symbol planes (with more than two symbols, for example three symbols: "0", "+1", "-1"). The reference Witten et al (Table I and Figure Ib) indicates how to handle the probabilities associated with more than two symbols. It should be noted that the invention makes it possible to evaluate the probability of the symbols in at least one symbol plane (preferably the plane of the most significant symbols), from a source model (signal to be encoded / decoded).

Moreover, 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. In this case, we can initialize the probabilities of the symbols 0, 1, + and -, starting from the value of the parameter α associated with the model. Moreover, as we have seen above, the invention makes it possible to optimize the contexts of the contextual arithmetic coding. In addition to the fact that 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.

More generally, the invention applies to any type of coding (Huffman, or others) based on the probabilities of symbols in symbol plane coding. Thus, the invention can be applied more generally to other types of entropy coding than arithmetic coding.

Moreover, the case of the generalized Gaussian model with transmission of the shape parameter has only been described above as an exemplary embodiment. Models other than the generalized Gaussian model are possible. For example, models of fixed probabilities (a Laplacian model in particular) or parametric models (alpha-stable models, Gaussian mixing models, or others) can also be considered to model the source.

More generally, it is possible not to model the signal distribution, but simply to compute the probability tables at the encoding based on the raw (unmodeled) distribution of the signal. One could then code these probability tables and transmit them to the decoder so that the latter does not have to recalculate them (deletion of the module 603 of FIG. 6 and reception of the probability tables instead of the form factor α). Nevertheless, it is preferred to model the distribution of the signal and to transmit to the decoder only a few parameters (in particular the form factor α) which characterize the model, as previously described, in order to limit the quantity of data in the coded stream.

Claims

A method of processing a signal for encoding / decoding in compression of the signal by symbol planes, wherein probabilities of symbol values are determined for at least one plane (Pκ-i), characterized in that said probabilities are dynamically calculated from an estimate (Mod) of a signal distribution (X).

2. Method according to claim 1, wherein the signal is quantized before coding, characterized in that the estimation of the signal distribution is conducted on the signal to be coded (X), preferably before quantization.

3. Method according to one of claims 1 and 2, characterized in that the distribution estimate of the signal comprises a modeling of the distribution of the signal (H), to derive at least one parameter (α) characterizing a model (Mod ) representing a density of probabilities (pdf) of the signal.

4. Method according to claim 3, characterized in that the modeling is performed at the coding (505), in that said parameter (α) is communicated for the purpose of decoding, and in that said probabilities are calculated, at the coding (507). ) and decoding (603) as a function of said parameter (α).

5. Method according to one of claims 3 and 4, characterized in that the model is generalized Gaussian type, and in that said parameter is a form factor (α).

The method according to any one of the preceding claims, wherein, the signal comprising a succession of values (a,), each value (a,) is decomposed into a plurality of symbol values (0; 1) in a plurality respective symbol planes (P _k ), said probabilities being calculated for at least one plane (MSB) and each aiming at the probability of having, in this plane, a symbol value equal to a given symbol, characterized in that said probabilities are calculated at least for the plane (MSB) ) representing the most significant symbol values.

7. Method according to claim 6, characterized in that said probabilities are further calculated for other planes (Pk), taking into account a context (C) defined by symbol values taken in planes (Pk + i, Pk + 2, • • -, Pκ-i) representing more significant symbol values.

8. Method according to claim 7, characterized in that, for the same signal value position (z) (a,) in said succession of values, each symbol value taken in a plane (Pk + i, Pk + 2 , • • -, Pκ-i) representing a symbol value more significant than a symbol value in a current plane (Pk), defines a context value (C) for this current plane (Pk) and for this position ( z), and in that said probabilities are calculated for the current plane (Pk) taking into account a plurality of possible values of the context (C) for the current plane (Pk).

9. Method according to claim 8, characterized in that a limited number of possible values of the context (C) is chosen.

Method according to claim 9, characterized in that the number of possible context values per symbol plane is limited to two:

a first context value designating the occurrence of at least one significant symbol value in the planes (Pk + i, Pk + 2, • • -, Pκ-i) representing more significant symbol values,

a second context value signifying that no significant symbol value occurrence has been found in the (Pk + i, Pk + 2, • • -, Pκ-i) planes representing more significant symbol values.

11. Encoder for implementing the method according to one of the preceding claims, characterized in that it comprises a module (505) for estimating a distribution of the signal to be encoded, supplying a module (507) calculation said probabilities of symbol values.

12. Decoder for implementing the method according to one of claims 1 to 10, characterized in that it comprises a module (603) for calculating said probabilities of symbol values, from an estimate (α) of a signal distribution.

13. Decoder according to claim 12, for implementing the method according to claim 4, characterized in that said module (603) for calculating said probabilities of symbol values is fed by at least one parameter (α) characterizing the model. probability density of the signal before coding, said parameter being received by the decoder.

14. Computer program intended to be stored in a memory of an encoder according to claim 11 or a decoder according to one of claims 12 and 13, characterized in that it comprises instructions for the implementation of the method according to one of claims 1 to 10, when executed by a processor of the encoder or decoder.