WO2008104725A1

WO2008104725A1 - Optimised algebraic encoding and decoding method, and related modules and computer software

Info

Publication number: WO2008104725A1
Application number: PCT/FR2008/050257
Authority: WO
Inventors: Stéphane RAGOT; Marie Oger; Marc Antonini
Original assignee: France Telecom
Priority date: 2007-02-21
Filing date: 2008-02-15
Publication date: 2008-09-04

Abstract

The invention relates to an encoding method that comprises a decomposition into bit planes (P0, Pϰ-1), after a quantification of the bit planes in an N-dimension quantification space (Λo) having an additive structure, while respecting the condition according to which p is a strictly positive integer such that the space 2pZN is strictly included in that quantification space. The method further comprises suppressing from the 0-rank bit plane (P0) a number of predetermined bits based on an error correction code including the zero-rank bit plane.

Description

OPTIMIZED ALGEBRATE CODING AND DECODING METHOD, COMPUTER MODULES AND COMPUTER PROGRAMS

The present invention relates to the field of signal encoding and decoding devices, intended in particular to take place in applications for transmission or storage of digitized and compressed signals. Such signals include, for example, audio signals, including speech signals, images and video.

FIG. 1 shows a coding device 106 and a decoding device 107. The coding device 106 is adapted to receive a signal S at its input, to code it and to output a bit stream φ comprising the data resulting from the coding of the signal. signal S. The decoding device 106 is adapted to receive the input bit stream φ, to decode it and to output a restitution of the signal S. In general, the coding device 106 comprises an analysis block 100, a block of quantization 101 and a lossless compression block 102, and the decoding device 107 comprises a lossless decompression block 103, an inverse quantization block 104 and a synthesis block 105. Depending on the type of signal S, the analysis performed by the analysis block

100 includes the calculation of the parameters of a model, for example a model of linear prediction, sinusoidal or prediction of motion, etc. and / or performs a transformation (Fourier, wavelet, etc ...). The analysis block 100 is optional. For example, in the case of PCM (PCM) coding, there is no analysis block.

The quantization block 101 performs a lossy compression operation, of the scalar or vector quantization type, of values associated with the signal that it receives as input. In the case of scalar quantization, these values are approximated by reconstruction levels (or representatives) defined in adjacent intervals; each of the intervals is represented by a unique reconstruction level which can be associated with a quantization index (integer). The lossless compression block 102 aims to eliminate the statistical redundancy existing in a signal after quantization. For example, it implements methods of the Huffman coding type, Golomb-Rice coding or arithmetic coding. The lossless compression block 102 is optional: in applications requiring a fixed bit rate, it complicates the implementation because it leads to a variable bit rate. The elements supplied at the output of the lossless compression block are inserted in a binary sequence according to a determined format. The binary sequence thus formed is then inserted into the bit stream φ. This bit stream φ is then received at the input of the decoding device

107, for example following a transmission on a transmission link disposed between the coding device 106 and the decoding device 107. If we consider that no error has been introduced during the transmission, the lossless decompression block 103, optional, reconstructs the information at the output of the quantization block 101. This information is then processed by the inverse quantization block 104, which reassigns a value instead of the quantized coefficient (for example, the inverse quantization assigns a point value in the range indicated by the quantized coefficient, for example that of the middle of the interval). The synthesis block 105 synthesizes a signal using, for example, excitation generation followed by filtering, inverse transformation, etc. In the case of the MIC coding in particular, this synthesis is omitted.

In the remainder of the document, particular attention is given to the operations performed at the level of quantization and lossless compression (if it exists) in the coding device 106, and to the corresponding operations performed at the decompression level without loss (if it exists) and inverse quantization, in the decoding device 107.

The invention relates more particularly to coding and decoding techniques known as "bit plane".

Such techniques are for example used in MPEG-4 audio coding, in particular by the Bit Sliced Arithmetic Coding (BSAC) coder (see the documents "Multi-Layer Bit-Sliced Scalable Audio Coding", S.-H. Park, YB Kim, YS Seo, 103th AES Convention, Sept. 1997, Paper 4520 and "Fine grain scalability in MPEG-4 Audio ", S.-W. Kim, S.-H. Park, and Y.-B. Kim, 111th AES Convention, Sept. 2001, Paper 5401).

Documents EP0884850, EP0918407, EP1431963, EP1463206 and EP1509904 also describe audio coding operations with scalar quantization followed by bit plane processing.

These bitmap coding techniques are also used in image coding or MPEG-4 FGS (Fine Grain Granularity) video coding.

The main advantage of bitmap coding is that it naturally leads to hierarchical coding of the signal, which allows the encoder to provide varied bit rates.

The binary data from the coding operation are divided into successive layers of variable size of decreasing importance. Each layer corresponds to binary codes describing all or part of a bit plane of a given rank and the relevant sign bits. In the event that the allocated bit rate is insufficient to transmit all the layers, the lower importance layers, that is to say those associated with the lower bit planes, are eliminated, the bit rate is thus reduced while retaining the most important layers, that is, those associated with higher-order bit planes.

Such coding thus enables the decoding device to make successive approximations of the signal of increasing precision, which are reconstructed as and when receiving additional portions of the bitstream from the coding device and relating to layers. lower level than previously received layers.

An example of operations performed by a bitmap coding device will be described below.

Let us consider a signal to be coded represented by X = [xi, ..., x _N ], with N> 1. The values Xi,..., X _N are, for example, N spectral coefficients obtained by time-frequency transformation and formatting (division by scale factor, for example) of a sampled signal time frame. A scalar quantization operation is first performed on the tuple X = [Xi, ..., X _N ]. The quantization space chosen is for example Z ^N = {[zi, ..., z _N ] / Σie 2, where E is the set of relative integers}

Thus the vector Y = [V ₁ , ..., y _N ] is the vector such that each quantization coefficient y _\ is the result of the "quantization" operation on the parameter Xi, that is to say that y \ is the rounding of Xi in S. The rounding of Xi in 2 could also be done with a "dead zone" around 0 (which is commonly called dead zone in English); here we treat only the case without dead zone, without loss of generality. A bit plane decomposition operation is then performed.

First, we distinguish the signs and the absolute values of the quantization coefficients, ie for i = 1 to N, y _t = (-l) ^s "χ", with Ci ₁ =

the

value a

Then the absolute values α _t are decomposed, with i = 1 to N, in binary form, ie: Ci ₁ = Ci _{1 KΛ} 2 ^KΛ + • • • + α _{t 1} 2 ¹ + α _{t 0} 2 °, where K is the minimum number of bit planes needed to break down of the absolute values, namely: £ = maχ (αrrsup [iog ₂ (maχ _{i = 1>> iV} α,)], l), where denotes rounding arrsup in upper integer and with Iog ₂ (θ) = -∞. We obtain by this decomposition the K vectors (binary)

P _k = [α _u • • • α _NJζ ] with k = 0, ..., K-1, and the sign vector (binary) S = [S ₁ • • • s _N ].

These vectors are of size N.

These vectors Pk constitute the bit planes determined for the signal

X. The vector P _k is called the plane of bits of rank (or weight) k. The higher bit plane Pκ-i is the most significant bit plane (MSB or Most Significant

Bits in English), while the lower bit plane Po is the least significant bit plane (LSB or Least Significant Bits).

Since the sign of zero is undefined, the above convention s, = 0 if y _t = 0 can be changed to ^ = I if y, = 0. In general, the bit planes obtained Pk with k = 0, ..., K-1 are then coded by sub-blocks, then the coding elements obtained are inserted in the binary sequence starting with the coding elements obtained for the upper bit plane P _κ- i _, and then taking the successive bit planes in an order of k decreasing. If the allocated bit rate allows it, the successive insertion of the coding elements for each bit plane to those obtained for the lower bit plane Po is continued.

The sign bits S ₁ , i = 1, ---, n, are inserted in the binary sequence only if the corresponding absolute value _t is non-zero. To enable decoding of the bit planes, even when only a part of the bit planes is received by the decoder, the sign bit S ₁ characterizing the sign associated with the value a-, is inserted into the bit sequence as soon as a coded bits {α _hk ) _{k = Q κ} 1 is _equal to 1. Thus, when the coding elements relating to the plane Pk are inserted in the binary sequence, data defining a vector S _k of variable size and which contains the signs associated with the values α _ι such that α _{ι k} is the first non-zero bit among α _{ι k} , α _{ι k + ι} ..., α _{ι K} _ _γ .

Figure 2 shows a bit plane decomposition for N = 8 and 7 = [-2, + 7, + 3.0, + 1, -3, -6, + 5]. In this case, K = 3, P ₀ = [0,1,1,0,1,1,0,1],

Pi = [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]. It is desirable to further improve the performance of the scalar quantization followed by bit plane coding, in particular by increasing the compression ratio, while minimizing the loss of information. For this purpose, according to a first aspect, the invention proposes a method of encoding a signal comprising the following steps, starting from N signal values with N> 1:

in a preceding step, defining a network of bit points of dimension N different from 2 ^P Z ^{N |} with p integer positive or zero;

in a quantization step, determining, for each of said values, an integer quantization index such as the vector of dimension N, having for coordinates said determined quantization indices, or element of said network of points; decomposing said quantization indices in binary form to form bit planes of length N;

in at least one of said bit planes, deleting at least one predefined position bit and thus forming at least one reduced plane; - Constitute a binary sequence from at least one reduced plane.

A network of points is a discrete set of points in the space R ^N = {ri, ..., r _N / ne R set of reals}, which has an additive group structure (the sum and the difference of two vectors - or points - any of the network is also a vector - or point - of the network, (see "Packing Sphere, Lattices and Groups", JH Conway and Sloane NJA, Third Edition, Springer-Verlag, 1999).

Point networks have many applications in telecommunications techniques: vector quantization, coded modulation and cryptography. The simplest network of points is the network Z ^N , also called cartesian grid or cubic network. This is associated with uniform scalar quantization. Other examples of networks are:

• The network D _N , in dimension N, defined by the equation:

NOT

D _N = {Y = ( _yi , -, y _N ) ≡ ZN Σ y, is even ι = l • The network RE _N = 2D _N , with N even, defined by the equation:

RE _N = 2D _N u {2D _N + (l, h - -, I)], where 2D _N = {Y = (2y _ι , - - -, 2y _N ) / (y _ι , - - -, y _N ) e Z ^N }.

Well-known particular cases are the network D ₄ called Schafli network and the network RE ^ called the Gosset network.

A network of points of dimension N, noted Λ, is called integer if its points have integer coordinates, in other words if Λc Z *. A particular class of whole networks is the class of bit-point networks. These admit as sub-network 2 ^P Z ^N , where 2 ^P Z ^N =

Y ^ y ₁ ^{,, Δ} y _N ^{) /} Ky ₁ ,, y _N > ^ ^ /. _c _'es t ie there p integer greater than or equal to 0 such that the assembly 2 ^P Z ^N A C≡. A method according to the invention thus advantageously takes advantage of the algebraic structure of the bit-point networks. At least one bit is eliminated in at least one bit plane without loss of useful information. The compression ratio obtained is therefore greater than conventional bitmap coding, and this by reducing the loss of information.

Using quantization in a bit-point network makes it possible to take advantage of the granular gain values offered by these networks, which reduces the loss of information. The granular gain measures the "efficiency" of the discretization of the space corresponding to a network of points. The quantization performance, measured in terms of mean squared error, is related to a quantity called "generalized second order moment" of the network (see JH Conway and NJA Sloane, Sphere Packing, Lattices and Groups, Third Edition, Springer -Verlag, 1999). For an entire network Λ, the generalized moment of order 2, denoted G (A), is a characteristic invariant Λ; it represents the granular quantization error in Λ (that is, the quantization error obtained when the uniform source is coded without "overloading").

We then define the granular gain as: γ _g (A) = 10 log ₁₀ - ^ -. For example,

G (A) γ _g (D ₄ ) = 0.42 dB and γ _g (RE) = 0.62 dB.

In one embodiment, the number of bits deleted is a function of the number of redundant bits of at least one determined block detector / corrector code of length N. This number of bits is chosen to be less than or equal to the number of redundant bits of at least one detector / corrector code block determined length N.

This arrangement makes it possible to eliminate redundant bits from the bit planes because of the algebraic structure of the bit network used for the quantization. The compression ratio achieved is even higher without loss of additional information.

In one embodiment, from M blocks of N values, with M strictly greater than 1: for each block of values, there are N quantization indices;

the set of M blocks of N indices is broken down into bit planes of length M * N. This decomposition in M blocks makes it possible to jointly code a number of values greater than N.

In one embodiment, in each bit plane of a plurality of said bit planes, a respective number of bits is omitted to form a plurality of reduced bit planes, the number of bits deleted in each bit plan being less than or equal to the number of redundant bits of a determined detector code and / or block error corrector of length N associated with said bit plane. A binary coding sequence of the signal is formed using coding elements defined according to at least reduced bit sets.

This arrangement makes it possible to eliminate the redundant bits for several bit planes, associated with respective error correcting codes, that is to say such that the bit planes are code code words that are detectors and / or correctors. errors. The number of bits deleted without loss of information is thus increased.

According to a second aspect, the invention proposes a coding module of a signal comprising: a quantizer adapted to determine, for each of N values defined as a function of the signal, an integer quantization index such as the vector of dimension N, having for coordinates, said determined quantization indices, ie element of a determined bit-point network, of dimension N different from 2 ^P Z ^{N |} with p integer positive or zero;

binary decomposition means adapted to decompose said quantization indices in binary form to form bit planes of length N;

suppression means adapted to eliminate, in at least one of said bit planes, at least one predefined position bit and thus form at least one reduced plane; means for constituting a binary sequence from at least one reduced plane. According to a third aspect, the invention proposes a computer program to be installed in a coding module of a signal, said program comprising instructions for implementing, during an execution of the program by means of processing said module. the following steps: in a quantization step, determining, for each of N values defined as a function of the signal, an integer quantization index such as the vector of dimension N, having as co-ordinates said determined quantization indices, ie element of a binary array of points of dimension N different 2 ^P Z ^{N |} with p positive or zero integer of said network of points;

decomposing said quantization indices in binary form to form bit planes of length N;

According to a fourth aspect, the invention proposes a method for decoding a binary sequence comprising coding elements, with a view to restoring N definition values of a signal, according to which:

according to coding elements included in the binary sequence and relating to at least one bit plane, determining a set of bits relative to said bit plane;

- Completing said set of bits with a number of additional bits whose respective values are defined as a function of the bits of said set of bits and a specific detector code and / or block error corrector, of dimension N, associated with said plane bits, to determine the given bit plane of dimension N;

calculating N quantization indices as a function of at least the respective N bits of the determined bit plane, such as the dimension vector N, having as coordinates said computed quantization indices, either element of a determined bit-point network of dimension N other than 2 ^P Z ^{N |} with p integer positive or zero;

determining N signal definition values as a function of at least the N quantization indices. According to a fifth aspect, the invention proposes a module for decoding a binary sequence, comprising:

means for, as a function of coding elements included in the binary sequence and relating to at least one bit plane, determining a set of bits relating to said bit plane; means for completing said set of bits with a number of additional bits whose respective values are defined as a function of the bits of said set of bits and of a determined N-dimensional block error detector and / or detector code, associated with said bit plane, for determining the bit plane of dimension N; means for calculating N quantization indices as a function of at least the respective N bits of the determined bit plane, such as the dimension vector N, having as coordinates said computed quantization indices, being element of a network of points determined binary of dimension N different from 2 ^P Z ^{N |} with p integer positive or zero;

means for determining N signal definition values as a function of at least the N quantization indices.

Other features and advantages of the invention will become apparent on reading the description which follows. This is purely illustrative and should be read with reference to the accompanying drawings, in which: FIG. 3 shows processing blocks of a coding module in one embodiment of the invention; FIG. 4 represents processing blocks of a decoding module in one embodiment of the invention; FIG. 5 represents a binary sequence constituted by the coding device of FIG. 1 in one embodiment of the invention; Fig. 6 is a flowchart showing steps of a decoding method in an embodiment of the invention; FIG. 7 represents a binary sequence constituted by the coding device of FIG. 1 in one embodiment of the invention; FIG. 8 is a flow chart showing steps of a decoding method in one embodiment of the invention.

The invention advantageously takes advantage of certain peculiarities specific to binary networks. As described in "Coset codes; I. Introduction and geometrical classification ", Forney, GD, IEEE Transactions on Information Theory, Volume 34, Issue 5, Part 1, Sept. 1988 Page (s): 1123 - 1151), a binary network Λ _o in N dimension including strictly a sub-network 2 ^P Z ^A ', with p strictly positive, is associated with one or more correction codes / block error detectors. Each of these detector / error correction codes is of the form [N, k, d] where N is the length or dimension of the code equal to the network dimension Λ _o , k is the number of independent symbols within the N symbols constituting a word of the code considered and d is the Hamming distance within the code. The values k and d vary according to the codes. For such a binary network Λ _o , there exists j determined positive integer, such that each element of the binary network can be written in the form:

^J 2 ^{+ p} y _p + _{j +} 2 ^{j + p "1} ₊ pi ⁺ yj 2 ... ^{j + 1} yj ₊ i + ^j +2 ^{2Vj" 1} y _H ⁺ - --2yi + y _0, where y _{j + p} , yj _{+ p-} i, ..., yj + i are elements of Z ^N and y, yj.i, ..., yi and y ₀ are respective error-correcting code words [ N, kj, dj], [N, kj.i, dj-i], ... [N, k ₀ , do]. A bit plane coding according to the invention comprises a quantization operation affecting a quantization vector Y = [yi, ..., y] element of the network Λ _o to an N-tuplet of values X = [Xi, .. ., X _N ] - Such quantification followed by a decomposition into bit planes gives rise to a plane P ₀ of rank 0 which is a code word of a detector / error correction code [N, k ₀ , do], and more generally if j> 0, gives rise to planes of rank 0 to J Po to Pj which are respective detector / error-correcting code code words [N, k ₀ , d ₀ ], ..., [N, kj, dj .

For example, the binary array D _N can be written as: D / v = 2Z ^N + [N, N-1, 2] = J2) / + c / y GZ ^w ; c ε [iV, JV - l, 2]}. The code [N, N-1, 2] is a parity code whose codewords comprise N bits, of which N-1 bits are independent and a bit (called parity bit) is deduced from the value of the N-bits. 1 other bits. This parity bit is redundant.

The RE _N binary network can be written in the form: RE _N = 4Z ^N + 2 [N, N-1, 2] + [N, 1, N]

= {φy + 2c + d I ye Z ^N ; ce [_V, _V - 1,2]; J e [_V, l, _V]} - The code [N, N-1, 2] is a parity code whose code words comprise N bits, of which N-1 are independent and one bit is redundant (that is to say that, as part of N-1 bits, the Nth bit can be determined without loss). The code [N, 1, N] is a repetition code whose codewords comprise N bits, of which 1 is independent and N-1 are redundant. The corrective codes / block error detectors considered are such that the number of redundant bits in the code is strictly greater than 0, because the bit network is different from a network of the form 2 ^P Z ^N.

An encoding method according to the invention further comprises at the encoder a step of reducing the number of bits, comprising the deletion of one or more redundant bits at predefined positions in at least one bit plane corresponding to a word of code of a detector code / error corrector. The number of bits deleted is a function of the number of independent symbols within the N symbols constituting a mode of the code. It is set equal to or less than the number of redundant (or dependent) symbols in a word of said detector / error corrector code. For example, in the case envisaged above where planes Po to Pj of rank 0 to j are detector code words / error correctors, with j> 0, we will proceed to a reduction of the number of bits in the different planes P ₀ to P _j Such coding thus makes it possible to reduce the number of bits necessary to code the signal, without any loss of additional information.

At the level of the decoder receiving coding elements relating to at least one bit plane in which one or more bits have been deleted according to an encoding method in one embodiment of the invention, these deleted bits are deduced, in a step bit plane extension, as a function of the bits received and the detector / error correction code to which belongs the bit plane considered.

Consider with reference to Figure 3, an encoder 1 in one embodiment of the invention.

This encoder 1 comprises in particular a quantization block 2 associated with a quantization space which is a bit network Λ _o , a bit plane decomposition block 3, a lower bit plane reduction block (s) 4 , a lossy compression block 5 and a binary sequence constitution block 6.

The binary network Λ _o of dimension N includes a sub-network 2 ^P Z ^N , with p strictly positive and the binary network Λ _o is different from WZ ^N.

In a first embodiment, choose as the binary network Λ _o the network D _N. Consider a signal to be coded represented by X = [X ₁ , ..., x _N ], with

N> 1. The values Xi,..., X _N are for example N spectral coefficients obtained by time-frequency transformation and formatting (division by scale factor, for example) of a sampled signal time frame.

A quantization operation is first performed by the quantization block 2 on the tuple X = [Xi, ..., X _N ], in order to determine the element Y = [yi, ..., y _N ] of D _N which is the nearest neighbor of X in D _N.

In one embodiment, the closest neighbor search in D _N is performed according to the fast algorithm for "D _n " (with n = N) described in the article "Fast quantizing and decoding and algorithms for lattice quantizers and codes Conway, J., Sloane, N., IEEE Trans. on Information Theory, Vol. 28, Issue 2, Mar. 1982, pages 227-232. This element Y is a vector of N-dimensional quantization comprising N quantization coefficients y _u i = 1 to N.

A bit plane decomposition operation is then performed by the bitmap decomposition block 3. As previously described, the signs and the absolute values of the coefficients of quantification are distinguished, ie for i = 1 to N, y, = (-iy 'x a,

[1 if y, <0 with a = y the absolute value of Vi and s = <

[0 if y _t > 0

Then we break down the absolute values at _t , with i = 1 to N, in binary form, that is: a _t = a _{ι KΛ} 2 ^KΛ + ••• + a _ιX 2 ¹ + a _ιfi 2 °, where K is the number of minimal bit planes necessary for the decomposition of the absolute values, ie: K = maχ (stop [Iog ₂ (maχ _{= 1; jJv} α,)], l), where arrsup is the rounding to the higher integer and with Iog ₂ (θ) = -∞.

We obtain by this decomposition the K bit planes Pk = Va _{1 k} ••• a _{N k} ] with k = 0, -, K -I, and the vector of signs S = [S ₁ ^{• • •} sv] ( it will be noted that in embodiments, the bit planes can be obtained as a function of alternative binary decompositions, for example following operations performed on the values a _ι as defined above, for example, in one embodiment , we can fix P _k = [l-α _li , - l -α _Λ , J, or a complementary representation to 2, or a Gray coding on the successive bit planes).

The K bit planes P _k , with k = 0, ---, K-1 and the sign vector S are then supplied to the lower bit plan (s) block 4.

Since Λ _o is the network D _N and therefore any bit plan P ₀ of rank 0 calculated during the quantization operation on D _N is a word of the parity code [N, N-1, 2] , block 4 suppresses N- (NI) = 1 bit of the plane P ₀ received.

In one embodiment, the last bit of the plane Po (corresponding to a _{N 0} ) is deleted. In another embodiment, a convention different is retained, and a bit in a different predefined position is deleted). This deletion is not accompanied by any loss of information since a number of bits equal to the number of redundant bits in the rank plane 0 has been removed. The bit plane of reduced rank 0, denoted Po ^* , containing N-1 bits, is then supplied to the block 5 of lossless compression, as well as the bit planes Pi to

Pκ-i containing N bits each and the sign vector S.

This lossless compression block 5 converts the bit planes (including the reduced plane Po) into a binary sequence. In the embodiment considered, it codes one by one the obtained bit planes Po ^* and P _k with k = l, ---, K-1, for example using a contextual arithmetic coding (cf. Arithmetic Coding for Data Compression, PG Howard and

JS Vitter, Proc. IEEE, vol. 82, no. 6, June, 1994) and he obtains the respective coding elements L (P ₀ ^* ) and L (P _k ) with k = 1, ---, K -1. The obtained coding elements, L (P ₀ ) and L (P _k ) with k = 1, ---, K-1, are then supplied with the sign vector S to the block 6 of bit sequence construction.

This binary sequence constitution block 6 then constitutes a binary sequence Seq1 relating to the coding elements determined for the signal X = [xi, ..., XN] considered.

With reference to FIG. 5, at the beginning of the binary sequence Seq1, it inserts, using a fixed number of bits, for example equal to 4, the number K of bit planes used, which is then equal to at most 15. (if the number K = 0, the coding is then finished). Then the coding elements L (P _κ- i), determined by the lossless compression block 5 for the plane P _κ- i _, are inserted into the binary sequence Seq1, followed by the partial vector of given signs Sκ-i (this step only takes place if K is greater than or equal to 2).

The partial vector of signs Sκ-i comprises the signs associated with the values a _t such that the bit a _{ι K} _ _ι is non-zero, with i = 1 to N.

Then the L (Pκ-2) coding elements, determined by the lossless compression block 5 for the P _κ plane. ₂ , are inserted as a result of the elements indicated above in the Seq1 sequence, followed by the partial vector of signs

Sκ-2-

The partial vector of signs Sκ-2 contains the signs associated with the values a _t such that a _{ι K 2} is the first non-zero bit among a _{ι K} _ ₂ and a _{ι K} _ _γ . Then according to an order of decreasing k, from k = K-2 to 1, the coding elements L (P _k ), determined by the lossless compression block 5 for the plane Pk, are inserted, followed by the partial vector of signs. Sk.

The partial vector of signs Sk contains the signs associated with the values a _t such that α _α is the first non-zero bit among a _{ι k} , a _ιMi ..., a _{ι K} _ _v . Finally, the coding elements L (Po), determined by the lossless compression block 5 for the reduced plane Po ^* , are inserted, followed by the partial vector of signs So.

The partial vector of signs So contains the signs associated with the values a _t such that a _ιfi is the first non-zero bit among a _ιfi , a _ιX ..., a _{ι KΛ} . In one embodiment, a bit stream Φ comprising the binary sequence Seq1 is transmitted to a decoder 10.

An encoding according to this first embodiment of the invention thus makes it possible to eliminate 1 bit among the N bits of the plane Po, without any loss of information, since only the redundant information has been suppressed. Let us now consider, with reference to FIG. 4, a decoder 10 in one embodiment of the invention. It is assumed here that the bit stream Φ has been transmitted without binary error and without rate reduction or frame loss. The decoder therefore receives the same information Φ as the information Φ sent by the coder. This decoder 10 includes in particular a lossless decompression block 11, a block 12 of lower bit plane (s) and a block 13 of inverse quantization.

The bit stream Φ comprising the binary sequence Seq1 is received by the decoder 10. The decoder 10 is adapted to carry out the following iterative steps, with reference to FIG. 6 and with the aid of the blocks 11 and 12. The decoder 10 first reads the number K of bit planes indicated at the beginning of the Seq1 sequence.

In an initialization step 1000, the value [0, ..., 0] is assigned to the vectors Y 'and S' of dimension N and the value K-1 is assigned to the variable k integer.

The decoder 10 extracts from the bit sequence Seq1 received the coding elements relative to the successive bit planes, from the bit plane higher than the lower bit plane, and supplies them to the lossless decompression block 11.

In a first step, the lossless decompression block 11 decodes the received coding elements corresponding to the sent coding elements L (P _κ- i) relating to the bit plane Pκ-i. It is assumed here that there are no binary errors on the channel and furthermore the channel has sufficient capacity to transmit the entire coding bit sequence. Thus the lossless decompression block 11 determines the bit plane P _κ- i. In a step 1004, it updates the value of Y 'by multiplying by 2 the current value Y' and adding to it the vector corresponding to the bit plane

Pκ-i

The sign data indicated in the partial vector of signs Sκ-i also extracted from the sequence Seq1 are exploited to update the vector of signs S '(step 1005), by adding the signs contained in the partial vector of signs. Sκ-i- For example, if Sκ-i indicates an index i, with i between 1 and N, such that the sign of a-, is positive, then the i ^th coordinate of S 'is kept at 0. if Sκ -i indicates an index i, with i between 1 and N, such that the sign of a-, is negative, then the i ^th S coordinate is updated to one.

The variable k is then decremented by 1 (step 1007), then the previous steps are repeated until k is different from 0 (test of step 1003).

When k reaches the value 0, the lossless decompression block 11 receives the coding elements L (P ₀ ) and decompresses them. It thus determines the bit plane Po ^* . The lower bit plane extension block (s) reconstitutes, in a step 1009, the Nth bit of Po from the received bit plane P ₀ ^* comprising N-1 bits.

In the embodiment considered, the plane P ₀ is reconstituted by adding a bit at the end of the reduced bit plane P ₀ ^* , ie P ₀ = [Po ^* , b], where b represents the parity of Po ^* , c that is, is equal to the sum of the N-1 bits of Po ^* modulo 2. This results from the fact that in D _N the plane Po corresponds to a code word of the parity code [N, N-1 , 2] (it is assumed here that the parity code is even parity). In another embodiment, in which the deleted bit would have been located at a position other than at the end of the bit plane Po, the added bit would have been inserted at the position corresponding to the deletion.

Then, in a last iteration of step 1004, the value of Y 'is updated by multiplying by 2 the current value Y' and by adding to it the vector corresponding to the bit plane Po The data of signs indicated in the partial vector of the signs So are exploited to update the sign vector S '(step 1005).

At this stage, the sign vector S 'thus calculated is equal to the sign vector S considered during the coding. The quantification vector Y considered during the coding is thus found in a step 1010, as a function of the values of signs indicated by the vector S 'and the value of the vector Y' finally determined. If Y = [yi, - -, YN] ₁ Y '= [y'i, ..., y'N] and S' = [Si, ..., s _N ], then y _t = (- l) ^s - xy \.

Then this quantization vector Y is supplied to block 13 for an inverse quantization operation.

In a second embodiment, the quantization space Λ _o chosen is the network RE _N - The steps implemented in such a case by the encoder 1 and the decoder 10 are described below. The signal to be encoded is represented by X = [xi, ..., x _N ], with N even> 2, which are for example N spectral coefficients obtained by time-frequency transformation of a sampled signal time frame. A quantization operation in the space RE _N is first performed by the quantization block 2 on the tuple X = [Xi, ..., X _N ], in order to determine the quantization vector Y ₂ = [ y ₂ i, ..., V _2N ], element of RE _N and which is the nearest neighbor of X. In one embodiment, the search for the nearest neighbor in

RE _N is carried out according to the principle of the fast algorithm for "Eg" described in the article "Fast quantizing and decoding and algorithms for lattice quantizers and codes", Conway, J., Sloane, N., IEEE Trans. on Information Theory, Vol. 28, Issue 2, Mar. 1982, pp. 227-232. A bit plane decomposition operation is then performed by the bit plane decomposition block 3, as a function of the N quantization coefficients y ₂ i, ..., y2N determined.

As previously described, the signs and the absolute values of the coefficients of quantification are distinguished, ie for i = 1 to N, y ₂ , = (-i) ^σ -xa,

1 if y _2ι <0 with a, = y _2ι the absolute value of y ₂ i and σ _t =

0 if y ,, ≥ 0

Then we decompose the absolute values at _t , with i = 1 to N, in binary form, that is: a _t = a _uKi _ _ι 2 ^{κ'1 ~ ι} + --- + a _ul 2 ^ι + a _{ι 0} 2 ° , where ST ₂ is the minimum number of bit planes necessary for the decomposition of absolute values, ie: K ₂ = maχ (α / rsup [Iog ₂ (maχ _{= 1 N} a _t )], l), where arrsup is the rounding up to the integer and with Iog ₂ (θ) = -∞.

We obtain by this decomposition the K ₂ bit planes π _k = [" _u --- a _{N k} ] with k = 0, ---, .ST ₂ - 1, and the vector of sign Σ = [σ _ι - --σ _N ].

K ₂ bit planes l ^~ l _k , with k = 0, ---, K ₂ -l and the sign vector Σ are then provided to the lower bit plan (s) block 4.

Since the quantization space is the network RE _N , any bit plane FIo of rank 0 calculated during the quantization operation on RE _N is a word of the repetition code [N, 1, N] and any plane of bits l ^~ li of rank 1 calculated during the quantization operation on RE _N is a word of the parity code [N, N-1, 2]. Therefore, when the quantization space is the RE _N network _, the lower bit plane reduction block (s) of the encoder 1 is adapted to suppress N- (NI) = 1 bit of the plane l ^~ li of rank 1 received and to delete N-1 bits of the plane Fl ₀ of rank 0 received. In the embodiment considered, the last bit of the plane l ^~ li

(corresponding to a _{N l} ) is deleted. In another embodiment, a different convention is retained, and a bit in another position is deleted. The bit plane of rank 1 thus reduced is noted l ^~ li ^* . It contains N-1 bits.

In one embodiment, the last N-1 bits of the FIo plane are deleted. In another embodiment, a different convention is retained, and bits in other positions are deleted.

The bit plane of rank 0 thus reduced, denoted Fl ₀ ^* , thus contains 1 bit

("I.o λ

The bit planes of rank 0 and 1 reduced, Fl ₀ ^* and Fl /, are then provided to the block 5 of lossless compression, as well as the sign vector Σ and the bit planes Fl ₂ to Flκ-i containing N bits. each.

In the same way as seen previously with reference to the first embodiment, the lossless compression block 5 then codes one by one the reduced bit planes FIo ^* and Fh ^* , and the bit planes FI _k with k = 2, - - -, K ₂ - 1 and obtain the respective coding elements L (FI ₀ ^* ), L (FlT) and L (Fl _k ) with fc = 2, - - -, J _{- 2} - I.

The obtained coding elements are then provided with the sign vector Σ at block 6 of bit sequence constitution.

This binary sequence constitution block 6 then constitutes a binary sequence Seq2 relating to the coding elements determined for the signal X = [xi, ..., XN] considered. With reference to FIG. 7, it indicates at the beginning of the binary sequence Seq2 using a fixed number of bits the number K ₂ of bit planes considered.

The partial vector of signs Σ _k contains the signs associated with the values a _t such that a _{ι k} is the first non-zero bit among a _{ι k} , a _{ι k + ι} ..., a _ι:, _R K, -l ' for k = 0, ---, K ₂ -l. The coding elements L (π-2 _K i) determined by the block 5 of lossless compression to the plane π 2 _K-i of rank K ₂ -I, are inserted into the bit sequence Seq2, followed by the partial vector signs E ^ _2-1 .

Then the coding elements L (π _K 2 -i) determined for the plane π _K 2 -i are inserted following the elements indicated above in the sequence Seq2, followed by the partial vector of signs Σ _Ki _ ₂ .

Then according to an order of k decreasing from k = K ₂ -2 to 2, the coding elements L (π _k ) determined by the lossless compression block 5 for the plane rik are inserted, followed by the partial vector of signs Σ k. The coding elements L (FIi) determined for the reduced rank plane 1 are inserted in the sequence Seq2, followed by the partial vector of signs Σi and finally the coding elements L (FI ₀ ) determined for the rank plane 0 reduced are inserted, followed by the partial vector of signs Σo.

In one embodiment, a bit stream Φ ₂ comprising the binary sequence Seq2 is transmitted to a decoder 10.

An encoding according to this first embodiment of the invention thus makes it possible to eliminate 1 bit among the N bits of the FIi plane and N-1 bits among the N bits of the FIo plane, without any loss of information, since only 1 redundant information has been removed. The bit stream Φ ₂ comprising the binary sequence Seq 2 is then received by the decoder 10.

In this second embodiment, the decoder 10 is adapted to implement the following iterative steps using the blocks 11 and 12. These steps are similar to those described above with reference to FIG. is for those who are in the rank 0 and 1 plans.

The decoder 10 reads first the number of bit planes K ₂ indicated at the beginning of the Seq2 sequence.

Then with reference to FIG. 8, in an initialization step 2000, the value [0,..., 0] is assigned to the vectors Y ₂ and Σ of dimension N and the value K ₂ - 1 is assigned to a variable k whole. The decoder 10 extracts from the bit sequence Seq 2 received the coding elements relating to the successive bit planes, from the bit plane higher than the lower bit plane, and supplies them to the lossless decompression block 11.

In a step 2002, the lossless decompression block 11 thus receives the coding elements L (π _K 2 -i) (it is considered here that there are no binary errors on the transmission channel and moreover that the channel has sufficient capacity to transmit all the coding binary sequence) and decompresses them. It thus determines the bit plane I ^~ lκ2-i-

Then, in a step 2004, if K ₂ -I is different from 0 and 1, it updates the value of Y ₂ by multiplying by 2 the current value Y ₂ (null vector) and by adding to it the vector corresponding to the plane of bits I ^~ lκ2-i In a step 2005, the sign data indicated in the partial vector sign Σ _κ ^ also extracted from the Seq2 sequence are used to update the sign vector Σ. The variable k is then decremented by 1 if it is different from 0

(step 2007), then the previous steps 2002, 2004, 2005 and 2007 are reiterated as long as k is different from 1 (test of step 2003).

When k reaches the value 1, in a step 2002, the lossless decompression block 11 receives the coding elements L (FI ₁ ) and decompresses them. It thus determines the bit map reduced Fl ₁ ^*.

Block 12 plane extension (s) of lower bits (s) reconstructs, in a step 2008, the Nth bit of Fl ₁ from the bit plane Fl ₁ ^* Reduced received comprising N-1 bits.

In the present embodiment, the Fh plane is reconstituted by adding a bit at the end of the reduced bit-plane Fh ^* or FIi = [Fh ^*, b '], where b' is the parity π / c ' that is to say is equal to the sum of the N-1 bits of FIi ^* modulo 2. This results from the fact that in RE _N the plane FIi corresponds to a code word of the parity code [N, N-1, 2] (it is assumed here that the parity code is even parity). Then a new iteration of step 2004, the Y ₂ value is updated by multiplying the value by 2 Y running and adding the vector corresponding to the bit plane Fl ₁ Signs of data shown in partial vector of signs Σi are exploited to update the sign vector Σ (step 2005).

Then k is decremented by 1 and thus reaches the value 0. In a step 2002, the lossless decompression block 11 receives the L (FI ₀ ) coding elements and decompresses them. It thus determines the reduced bit plane Fl ₀ ^* .

The lower bit plan extension block (s) reconstitutes, in a step 2009, the last N-1 bits of F1 ₀ ^* from the reduced bit plane F1 ₀ ^* received comprising 1 bit.

In the embodiment considered, the plane FIo is reconstituted by duplicating N times Fl ₀ ^* , ie Fl ₀ = [Fl ₀ ^* , Fl ₀ ^* ..., Fl ₀ ]. This results from the fact that in RE _N , the plane FIo corresponds to a code word of the repetition code [N, 1, N].

Then in a last iteration of the step 2004, the value of Y ₂ is updated by multiplying by 2 the current value Y ₂ and by adding to it the vector corresponding to the bit plane FIo The data of signs indicated in the partial vector of signs Σo are exploited to update the sign vector Σ (step 2005).

The quantification vector Y ₂ is thus found in a step 2010, as a function of the sign values indicated by the sign vector Σ and the value of the vector Y ₂ finally determined. If Y ₂ = [y _2Λ , ..., y _2ιN ], F ₂ = [J _{2 1} , ..., J _2JV ] and Σ = [σi, ..., O _N ], then y _u = ( -l) ^σ - χ y _{2> 1} .

In a step 2011, we check the parity agreement between the rank plane 1 FIi and the sign vector Σ. If K ₂ > 1, Flo ^* = [1] and if the parity of Σ is odd, then the plane FIi of rank 1 is replaced by [Fh ^* , b '], where b' is the complement of the bit b 'calculated previously. The values of Y ₂ and Y ₂ are then recalculated accordingly. This arrangement makes it possible to respect the algebraic constraints of the network RE _N.

It has been considered above in the two embodiments described above that no information was lost during the transmission phase. Nevertheless, in the event of loss of information, a decoding method according to the invention can nevertheless be implemented on the basis of the information actually received by the decoder 10. Techniques conventional ways to manage and / or restore lost information may further be implemented.

In the case where a part of the bit sequence has to be truncated before transmission, for example due to an insufficient bit rate available on the transmission link, a portion of the bit sequence Seq1, comprising lower level bit planes, is deleted. of the flow. This portion includes the least significant coding elements. The decoding is then done in a conventional manner at the decoder, taking into account only the higher level bit planes actually received in the bit sequence and the received parts of the lower bit planes.

An encoding method according to the invention allows the implementation of a hierarchical coding of the signal.

All or some of the processes implemented by the encoder 1 are in one embodiment implemented following the execution of computer program instructions on the calculation means of the encoder 1.

Similarly, all or some of the processing implemented by the decoder 10 are in one embodiment implemented following the execution of computer program instructions on calculating means of the decoder 10. In the first mode implementation of the invention described above in the quantization space D _N , a bit was deleted on the N bits included in the bit plane of rank 0. For example if N = 280 (corresponding for example to the number of samples in a useful band 50-7000Hz of the spectrum of an audio signal sampled at 16kHz over 20ms), one bit is removed on N = 280 bits included in the bit plane of rank 0 after quantization in the space D ₂₈ o-

In another embodiment, the N values of the signal Xi,..., X _{N are distributed} in p blocks of n values (N = pxn) and a method according to the invention is implemented on each set of values of size n. For example, in the case N = 280, we choose the number of blocks p equal to 14 and the dimension n of each block equal to 20. The quantization then takes place in the quantization space D.sub.0. bit in each plane of rank 0 calculated for each block. 14 bits are thus removed from the 280 bits corresponding to the 14 bit planes of rank 0.

In such a case, the bit sequence successively comprises the coding elements for each of the p = 14 bit planes of maximum rank, followed by the coding elements for the 14 bit planes of each rank in a descending order of order and terminates by the coding elements for the 14 reduced bit planes of rank 0.

These coding elements for the 14 reduced bit planes of row 0 comprise, for example successively, the coding elements defined according to the invention for the row plane 0 of the first reduced block according to the invention, and then the coding elements defined according to FIG. invention for the reduced rank plane 0 of the second block, etc., to the coding elements defined according to the invention for the reduced rank plane 0 of the fourteenth block.

Thus increasing the number of sub-blocks by decreasing the dimension n of the space D _n considered (n being also the size of each bit plane) makes it possible to increase the number of bits to be deleted without loss of information.

Nevertheless, the granular gains of the networks D _n or RE _n increase with the dimension n up to a maximum, then decrease. Thus the number M of selected blocks is actually a compromise allowing a number of bits deleted satisfactory while ensuring a sufficient granular gain.

In another embodiment, M blocks each comprising N defined values as a function of the signal are considered. N-dimensional bit planes are defined for each of the M blocks, then bit plane reductions are performed for each of the blocks. The bit sequence can then comprise only once the number of bit planes considered common to the M blocks, then the coding elements for the M bit planes of maximum rank, etc. to the coding elements for the M bit planes. rank 0 reduced.

In one embodiment, the binary representation of the bit planes can be reversibly modified before lossless coding, for example by complement representation at 2 or else by Gray coding.

In one embodiment, the higher bit planes that are not detector / error correction code words are jointly encoded by a technique such as stack-run integer sequence coding which is described in the article "Stack-Run Image Coding", MJ Tsai, JD Villasenor and F. Chen, IEEE Trans. Syst. Circuits Video Technol., Vol. 6, pp. 519-521, Oct. 1996.

In one embodiment, only the binary coordinates of rank 0 to jo, 3ij, i = 1 to N and j = 0 to jo, with jo strictly less than K, are calculated to determine the bit planes associated with detector codes. / error correctors. And for each y _h the difference between the absolute value of

and the term a _{1] o} 2 ^} ° + ••• + a _ιX 2 ^ι + a _{ι 0} 2 °. This difference is then encoded before insertion into a binary sequence. Only bit planes of lower ranks 0 to jo are then inserted in the bit sequence.

In the embodiments described, a maximum number of bits, equal to the number of dependent bits in a word of the detector / corrector code considered, were deleted in the bit plane associated with the detector / corrector code without loss of information. Of course, depending on the embodiments, a number of bits less than the maximum number may be deleted.

Claims

A method of coding a signal, comprising the following steps, starting from N values defined according to the signal, with N> 1:

in a preceding step, defining a bit-point network (Λo) of dimension N different from 2 ^P Z ^{N |} with p integer positive or zero; in a quantization step, determining, for each of said values, an integer quantization index such as the vector of dimension N (Y), having as its coordinates said determined quantization indices, or element of said network of points;

decomposing said quantization indices in binary form to form bit planes (Po,..., Pκ-i) of length N;

in at least one (P ₀ ) of said bit planes, removing at least one predefined position bit and thus forming at least one reduced plane;

(Po ^* );

- Constitute a binary sequence (Seq1) from at least one reduced plane (P ₀ ^* ).

2. The method according to claim 1, wherein the number of bits deleted, to form a reduced plane (Po), is less than or equal to the number of redundant bits of a determined detector code and / or block error corrector. length N.

3. Method according to claim 1 or 2, according to which, from M blocks of N values defined as a function of the signal, with M strictly greater than 1: for each block of values, there are N quantization indices; the set of M blocks of N indices is broken down into bit planes of length M * N; in at least one of said bit planes, at least one predefined position bit is eliminated and thus form at least one reduced plane;

a binary sequence is formed from at least one reduced plane.

4. Process according to any one of claims 1 to 3, according to which:

in each bit plane of a plurality (Fl ₀ , l ^~ li) of said bit planes, a respective number of bits is eliminated, to form a plurality of reduced bit planes (Fl ₀ ^* , FV), the number of bits deleted in each bit plane being less than or equal to the number of redundant bits of a determined detector code and / or block error corrector of length N associated with said bit plane;

a signal-encoding binary sequence (Seq 2) is formed using coding elements defined as a function of at least reduced bit sets (Fl ₀ ^* , l ^~ li ^* ).

5. Module (1) for encoding a signal comprising:

a quantizer (2) adapted to determine, for each of N values defined as a function of the signal, an integer quantization index such as the vector (Y) of dimension N, having for coordinates said determined quantization indices, or element of a determined bit network (Λo) of dimension N other than 2 ^P Z ^{N |} with p integer positive or zero;

binary decomposition means (3) adapted to decompose said quantization indices into binary form to form bit planes (Po,... Pκ-i) of length N;

suppressing means (4) adapted to eliminate, in at least one (P ₀ ) of said bit planes, at least one predefined position bit and thus form at least one reduced plane (P ₀ ); means (6) for constituting a binary sequence from at least one reduced plane (P ₀ ).

Computer program to be installed in a module (1) for coding a signal, said program comprising instructions for implementing, during a program execution by means of processing said module the following steps:

in a quantization step, determining, for each of N values defined as a function of the signal, an integer quantization index such as the vector (Y) of dimension N, having for coordinates said determined quantization indices, being an element of a bit network (Λo)) of dimension N other than 2 ^P Z ^{N |} with p positive or zero integer of said network of points;

(Po ^* );

7. A method for decoding a binary sequence (Seq1) comprising coding elements, for the purpose of restoring N definition values of a signal, according to which: - as a function of coding elements included in the binary sequence and relative at least one bit plane (Po), determining a set (PO ^* ) of bits relative to said bit plane;

- complete said set of bits (Po) with a number of additional bits whose respective values are defined as a function of the bits of said set (Po) of bits and a detector code and / or determined block error corrector, of dimension N, associated with said bit plane, for determining the bit plane (Po) of length N;

calculating N quantization indices as a function of at least the respective N bits of the determined bit plane, such as the dimension vector

N, having as coordinates said computed quantization indices, being element of a determined bit network (Λ _o ) of dimension N different from 2 ^P Z ^{N |} with p integer positive or zero;

determining N signal definition values as a function of at least the N quantization indices.

The decoding method according to claim 7, wherein:

according to coding elements included in the binary sequence (Seq2) and relating to bit planes (Fl ₀ , l ^~ li), determining a plurality of sets (Fl ₀ ^* , FV) of bits, each set of bits corresponding to a respective bit plane (Fl ₀ , Fh) of length N;

- complete each set of bits of said plurality of bit sets with a number of additional bits whose respective values are defined according to the bits of the corresponding set of bits and a detector code and / or error corrector in defined blocks, of dimension N, associated with said bit plane, for determining said plurality of bit planes (FI ₀ , Fh);

calculating N quantization indices as a function of at least the determined bit planes, such as the dimension vector N, having as coordinates said calculated quantization indices, or element of a determined bit-point network of dimension N different from 2 ^P Z ^{N |} with p integer positive or zero;

9. decoding module (10) of a binary sequence (Seq1), said module comprising:

means (11) for, as a function of coding elements included in the binary sequence and relating to at least one bit plane (FIo), determining a set of bits (FIo) relative to said bit plane;

means (12) for completing said set of bits (FIo) with a number of additional bits whose respective values are defined as a function of the bits of said set of bits and a detector code and / or block error corrector determined, of dimension N associated with said bit map, to determine the bit-plane (Fl ₀₎ of dimension N;

means for calculating N quantization indices as a function of at least the respective N bits of the determined bit plane, such as the dimension vector N, having as coordinates said computed quantization indices, being element of a network of points determined binary of dimension N different from 2 ^P Z ^{N |} with p integer positive or zero;

means (13) for determining N signal definition values as a function of at least the N quantization indices.

10. Computer program to be installed in a decoding module (10) of a binary sequence (Seq1), said program comprising instructions for implementing the following steps during a program execution by processing means of said program module: - according to coding elements included in the binary sequence

(Seq1) and relating to at least one bit plane (Po), determining a set (Po) of bits relative to said bit plane;

- supplementing said set of bits with a number of additional bits whose respective values are defined as a function of the bits of said set (Po) of bits and a specific detector code and / or block error corrector, of dimension N, associated with said bit plane, for determining the N-dimensional bit plane (Po);

calculating N quantization indices as a function of at least the respective N bits of the determined bit plane, such as the dimension vector N, having for coordinates said calculated quantization indices, that is element of a bit-point network (Λ _o ) determined of dimension N different from 2 ^P Z ^{N |} with p integer positive or zero;