FR2785742A1 - Coding method that takes into account predetermined integer equal to or greater than 2, number greater than or equal to 1 of sequences of binary data representing physical quantity - Google Patents

Abstract

Coding method takes into account preset integer equal or greater than 2, number, greater than or equal to 1, of binary data sequences of physical quantities. Each sequence has polynomial being multiple of preset polynomial and several binary data equal to product of any integer number M and integer NO, smallest integer so that given polynomial is divisible by each of the other polynomials.

Description

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 The present invention relates to a coding device, an encoding method, a device and a decoding method and systems implementing them.

 It applies both to the coding of data representative of a physical quantity, to the coding of data in the form of codes capable of modulating a physical quantity, to the decoding of data modulated signals, and to the decoding of data representative of physical quantities. . These data can, for example, represent images, sounds, computer data, electrical quantities, stored data.

 The invention finds application in the field of convolutional codes. When these are used to implement iterative decoding, these codes are greatly improved when their encoders contain a permutation device. In this case, they are usually called "turbocodes" and the corresponding iterative decoder is called "turbodecoder".

 On these subjects, documents which serve as reference are, on the one hand, the article of MM. C. BERROU, A. GLAVIEUX and P. THITIMAJSHIMA entitled "Near Shannon limit error-correcting coding and decoding: turbocodes" published with the proceedings of the conference "ICC'93", 1993, pages 1064 to 1070, and of on the other hand, the article by MM. C. BERROU and A. GLAVIEUX entitled "Near Optimum error-correcting coding and decoding: turbo-codes" published by IEEE Transactions on Communication, Volume COM-44, pages 1261 to 1271, October 1996.

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 However, the formation of permutation devices is far from being perfectly controlled. In general, this device uses square or rectangular matrices in which one line is written after the other and one column is read after the other. These matrices are generally very large, for example 256 x 256.

par le Jet Propulsion Laboratory, avec'TDA Progress Report", numéro 42-122, le 15 août 1995, MM. DOLINAR et DIVSALAR considèrent les permutations qui, en numérotant les k positions d'information entre 0 et k-1, déplacent les informations binaires placées en une position i jusqu'à une position e i + f, pour des valeurs "bien choisies" de e et de f. According to another method, in an article entitled "Weight distributions for turbo-codes using random and nonrandom permutations" published

by the Jet Propulsion Laboratory, with 'TDA Progress Report', number 42-122, on August 15, 1995, Messrs DOLINAR and DIVSALAR consider the permutations which, by numbering the k information positions between 0 and k-1, move the binary information placed in a position i to a position ei + f, for "well-chosen" values of e and f.

 In this document, they give only one example where k is a power of 2. Moreover, they do not discuss the possible reciprocal influence of the choice of the permutation device and that of the elementary convolutional encoders (2.1) to use to generate the coded sequences produced by the turbo encoder (3.1).

 The evaluation of the corresponding turbocode consists in simulating its use on a transmission channel with different signal / noise ratio values and in measuring the minimum value of this ratio for which a predetermined value of error probability on the binary values is reached.

 However, the use of simulations as an evaluation tool can lead to some problems.

 Consider, for example, the permutation device with k = 65536 = 256 x 256, discussed above, and choose a predetermined error probability equal to 10-5 to simulate the performance of a turbocode using this device. As a result, the average number of errors on binary values per block of 256 x 256 will be close to 1, but we will not know if each binary information has the same probability of error. This probability of error could be quite high for binary values with a

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 "unfortunate" position in the permutation device and this probability could be much smaller for more "happy" positions.

 A possible way to remedy this situation is to achieve a harmonious and joint design of the permutation device and the two convolutional encoders to ensure a reasonable uniformity of the error rate on the binary values after decoding, depending on the position of the binary information in the permutation device.

 Another problem is the lack of algebraic tools for specifying permutation devices. It would be useful to have means for specifying a selection of permutation devices having performance representative of the set of all permutation devices.

u = (uo, U1, Uk-1), appelées "séquences d'information", que l'on va coder en un triplet de séquences binaires,

v = (a, b, cl, chacune de ces séquences a, b et c, étant, à elle seule, représentative de la séquence u. The invention mainly relates to the transmission of information represented by sequences of binary symbols:

u = (uo, U1, Uk-1), called "information sequences", which will be coded into a triplet of binary sequences,

v = (a, b, cl, each of these sequences a, b and c being, by itself, representative of the sequence u.

représenter une séquence u, la forme u = (UO, U1, ..., Uk-1), et la forme polynomiale associée : u(x) = uo x + u1 x' + ... + Uk-1 x-'. In the rest of the description, it is used indifferently for

represent a sequence u, the form u = (UO, U1, ..., Uk-1), and the associated polynomial form: u (x) = uo x + u1 x '+ ... + Uk-1 x- .

triplet v = (a, 6, 0 : - de choisir a(x) = u(x) ; - de choisir b(x) = u(x).hi(x) lg(x), où g(x) est un polynôme, par exemple g(x) = + x + x3, correspondant, selon la représentation en séquence, à la séquence (1, 1, 0, 1) ;

et hi(x) est un polynôme, par exemple hJ(x) = 1 + x + x2 + X3@ correspondant à la séquence (1, 1, 1, 1) ; et Equivalent notations will be used for sequences a, b and c. Using this second representation, he is known to determine the

triplet v = (a, 6, 0: - choose a (x) = u (x); - choose b (x) = u (x) .hi (x) lg (x), where g (x) is a polynomial, for example g (x) = + x + x3, corresponding, in the sequence representation, to the sequence (1, 1, 0, 1);

and hi (x) is a polynomial, for example hJ (x) = 1 + x + x2 + X3 @ corresponding to the sequence (1, 1, 1, 1); and

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 by calling a sequence formed by permutation of the binary data of the sequence a, to choose c (x) = a * (x) .h2 (x) / g (x) where h2 (x) is a polynomial, by example h2 (x) = (1 + x2 + x3) corresponding to the sequence (1, 0, 1, 1).

 Any choice of the polynomials g (x), hi (x), h2 (x) and the permutation specifying the interleaver that associates the permuted sequence a * with the sequence a, specifies an encoder that we will call "turbo encoder". The set of sequences that a specified turbocharger can produce will be called "turbocode".

 In the following description, the term "first encoder", the elementary recursive convolutional encoder that produces the sequence b and "second encoder", the one that produces the sequence c.

 The polynomial divisions implemented are of the division type according to the increasing powers, well known to those skilled in the art. They use the modulo 2 arithmetic. The sequences a, b and c are binary sequences and in the general case the divisions which define b and c have a remainder.

 This type of coding method has the advantage of being suitable for iterative decoding that is efficient, inexpensive and inexpensive.

I/ Comment choisir les polynômes g(x), h1(x) et h2(x) ?
III Comment choisir la permutation des termes de la séquence a qui produit la séquence a* ? Parmi les choix proposés, trois exemples d'entrelaceurs, c'est-à-dire d'opérateurs qui permutent les termes de la séquence a, pour former la séquence a*, sont donnés ci-dessous :
A) dans le premier exemple, après avoir rangé les termes de a dans un tableau rectangulaire, successivement ligne par ligne et, pour chaque ligne, de gauche à droite, on forme la séquence a* en prélevant dans ce tableau successivement les termes colonne après colonne et, pour chaque colonne, de haut en bas. Par exemple, dans le cas de séquences de six termes et d'utilisation d'un tableau de deux lignes de trois To implement it, several questions arise:

I / How to choose the polynomials g (x), h1 (x) and h2 (x)?
III How to choose the permutation of the terms of the sequence to which the sequence a *? Among the choices proposed, three examples of interleavers, that is to say operators that permute the terms of the sequence a, to form the sequence a *, are given below:
A) in the first example, after arranging the terms of a in a rectangular array, successively line by line and, for each line, from left to right, the sequence a * is formed by taking in this array successively the terms column after column and, for each column, from top to bottom. For example, in the case of sequences of six terms and use of an array of two lines of three

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 columns, the interleaver transforms the sequence a = (ao, a1, a2, a3, a4, a5) into the sequence a * = (ao, a3, a1, a4, a2, a5).

 B) in a second example, the second term (i = 0, 1, 2, ...) a * j of the sequence a * is chosen as the term a, of the sequence a, with j = si + t calculated modulo the number of terms of the sequence a, s and t being integers. For example, if the number of terms of the sequence a is six and if s = 5 and t = 3, the interleaver transforms the sequence a = (ao, a1, a2, a3, a4, a5) into the sequence a * = (a3, a2, a1, ao, a5, a4).

 C) in the third example, the permutation chosen is random.

NI / How to avoid that the division defining b (x) has a remainder? and
IV / How to avoid that the division defining c (x) presents a remainder?
Answering these last two questions amounts to solving a problem frequently mentioned in the turbocode literature which is that of the "return to the zero state" of the elementary convolutional encoders defining b and c. Since the turbochargers have two elementary recursive coders, the second of which uses a permutation a * of the sequence a, it is desired to guarantee that the polynomials a (x) and a * (x) representing the information sequence u (x) are simultaneously divisible. by g (x). To assure this condition of divisibility of a (x) is simple because it is enough to build a (x) starting from u (x) by completing u (x) by stuffing symbols in number equal to the degree of g (x) and whose sole function is to guarantee the absence of remainder in the division used to produce b (x) from a (x).

 Choosing a permutation producing a * (x) from a (x) which guarantees both the divisibility of a * (x) per g (x) and good error correction performance for the turbocode thus specified is, on the other hand, more difficult.

 This problem can lead to disparities between the error probabilities after decoding the different bits constituting u (x).

 In an article published in Volume 31, No. 1 of the journal "Electronics Letters" on January 5, 1995, MM. BARBULESCU and PIETROBON

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 state that an interleaver can be described by successively and cyclically ordering the terms of the sequence a in a number of sequences equal to the degree of the polynomial g (x) incremented by one, and that, in this case, permutations internal to each of the sequences thus formed result in equality between the rest of the division defining the sequence b and that of the division defining the sequence c.

affirmation n'est vraie que si le polynôme g(x) est de la forme 11=0 à m 1. However, and contrary to what is said in this article, this

affirmation is only true if the polynomial g (x) is of the form 11 = 0 to m 1.

 In an article entitled "Turbo-block-codes" and published with the proceedings of the seminar "turbo coding" organized by the Institute of Technology Lund (Sweden) (Department of Applied Electronics) in August 1996, MM. C. BERROU, S. EVANO and G. BATTAIL expose that, by arranging the terms of the sequence u, cyclically, in a number of columns equal to a multiple of the degree NO of the polynomial of the type xn-1 of lower degree strictly positive which is divisible by g (x), permutations internal to each of the columns thus formed cause that the sum of the remainder of the division defining the sequence b and that of the division defining the sequence c is zero, so that the concatenation of the sequences is divisible by g.

 This document, like the previous one, therefore restricts the choice of interleavers to particular forms working independently on subsets of the terms of the sequence a by applying to them internal permutations. It does not guarantee, however, that individually a (x) and a * (x) are divisible by g (x). Only the divisibility by g (x) of the polynomial representing the concatenation (a, a *) of putting the two sequences a and a * end to end is guaranteed.

 It follows a possible loss of efficiency of the decoder since it is not informed of the state that had the encoder at the moment marking the end of the calculation of b and the beginning of the calculation of c.

 None of the cited articles offer an effective choice of interleaver.

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 The present invention intends to remedy these drawbacks by proposing, on the one hand, families of interleavers which guarantee the return to zero at the end of the sequence c, when the sequence b returns to zero and, on the other hand, proposing a wider choice of interlacers than the one proposed by the articles cited above.

entier tel que le polynôme V +1 soit divisible par chacun des polynômes g,(x) ; 2/ il comporte une première opération de production d'un nombre K*M1 de

séquences dites permutées , a,*, (i=1,...,K ; j=1,...,M1), chaque séquence a,,* - étant obtenue par une permutation de la séquence a, correspondante, ladite permutation étant, dans une représentation où les données binaires de chaque séquence a, sont écrites, ligne par ligne, dans un tableau à NO colonnes et M lignes, la résultante d'un nombre quelconque de permutations dites élémentaires qui, chacune : # soit a la propriété de transformer le code cyclique de longueur NO et de polynôme générateur g,(x) en un code

cyclique équivalent de polynôme générateur g,j{x) pouvant être égal à g,(x), et agit par permutation sur les NO colonnes du tableau représentant a,, For this purpose, according to a first aspect, the present invention aims a coding method characterized in that 1 / ilil it takes into account: - a predetermined integer M1, equal to or greater than 2, - a number K, greater than or equal to 2, of sequences a, (i = 1, ..., K) of binary data representative of a physical quantity, each sequence a, having: # a polynomial representation a, (x) multiple of a polynomial g, ( x), and # a number of binary data equal to the product of any integer M by the integer NO, smaller

integer such that the polynomial V +1 is divisible by each of the polynomials g, (x); 2 / it comprises a first operation of producing a number K * M1 of

sequences said permuted, a, *, (i = 1, ..., K; j = 1, ..., M1), each sequence a ,, * - being obtained by a permutation of the sequence a, corresponding, said permutation being, in a representation where the binary data of each sequence a, are written, line by line, in an array with NO columns and M lines, the resultant of any number of so-called elementary permutations which, each: # is a the property of transforming the cyclic code of length NO and generator polynomial g, (x) into a code

cyclic equivalent of generator polynomial g, j {x) may be equal to g, (x), and acts by permutation on the NO columns of the array representing a,

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redondantes dont la représentation polynomiale est égale à E f,,(x) cij(x), pour j=1,...,M9, chaque polynôme f,,(x) étant un polynôme de degré au plus égal au degré du polynôme g,J(x) de mêmes indices i et j. # is any permutation of the symbols of a column of that array; and - having, accordingly, a polynomial representation a ,, * (x) which is equal to a polynomial product c ,, (x) g ,, (x), - at least one permuted sequence aij * being different from the sequence a, corresponding, 3 / it comprises a second operation of production of M1 sequences

redundant whose polynomial representation is equal to E f ,, (x) cij (x), for j = 1, ..., M9, each polynomial f ,, (x) being a polynomial of degree at most equal to the degree of polynomial g, J (x) of the same indices i and j.

 Above are introduced, in a representation where the binary data of the sequence a are classified in a table of NO columns and M lines, the succession of permutations taken in the set of permutations comprising, on the one hand, the automorphisms of the binary cyclic code of length NO and of generator polynomial g (x), permuting between them at least two of the NO columns of the array and, on the other hand, permutations working only on data of the same column and permutating between they at least two of said data.

 The inventors have discovered that all these permutations, and only these, guarantee that for every polynomial a (x) whose division by g (x) leaves a zero remainder, the permuted polynomial a * (x) has the same property. .

 For the study of the conditions governing the choice of g ,,, the reader will be able to refer to the page 234 of the book of Mrs. FJ MAC WILLIAMS and MNJA SLOANE "The theory or error-correcting codes" published by the publisher North-Holland in 1977 and whose seventh printing took place in 1992).

 All the choices described in the present invention include the interleavers exposed in the two articles mentioned above. Thus the performance expressed in terms of error rate as a function of the signal / noise ratio can be improved without increasing the complexity of the turbo encoder or that of the turbo decoder.

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- un nombre K, supérieur ou égal à 2, de séquences a, (i=1,...,K) de données binaires représentatives d'une grandeur physique, chaque séquence a, possédant : # une représentation polynomiale a,(x) multiple d'un polynôme g,(x) prédéterminé et sans facteurs polynomiaux multiples, et # un nombre de données binaires égal au produit d'un nombre entier impair M quelconque par l'entier NO, plus petit entier tel que le polynôme xN0+1 soit divisible par chacun des polynômes g,(x) ; 2/ il comporte une première opération de production d'un nombre K*M1 de

séquences dites permutées , a,,*, (i=1,...,K ; j=1,...,M9), chaque séquence a,,* possédant une représentation polynomiale égale à a,,*(x)=a,*(xe) modulo (x"+1), où - n est le produit du nombre M par l'entier NO, - e,, est un nombre relativement premier avec n

- cI} est le quotient de a,,*(x) par g,J(x), - le polynôme g,,(x) est le polynôme générateur du plus petit code cyclique de longueur NO contenant le polynôme g1(xeIJ) modulo (xN0+1), au moins une séquence permutée aIJ* étant différente de la séquence a, correspondante ; 3/ il comporte une deuxième opération de production de M1 séquences redondantes dont la représentation polynomiale est égale à E f,,(x) c,,(x), pour j=1,...,M1, chaque polynôme f,,(x) étant un polynôme prédéterminé de degré au plus égal au degré du polynôme g,,(x) de mêmes indices i et j. According to a second aspect, the present invention aims at a coding method characterized in that: 1 / it takes into account: a predetermined integer M1, equal to or greater than 2,

a number K, greater than or equal to 2, of sequences a, (i = 1, ..., K) of binary data representative of a physical quantity, each sequence a, having: # a polynomial representation a, (x ) multiple of a predetermined polynomial g, (x) and without multiple polynomial factors, and # a number of binary data equal to the product of an odd integer M by the integer NO, smaller integer such that the polynomial xN0 +1 is divisible by each of the polynomials g, (x); 2 / it comprises a first operation of producing a number K * M1 of

sequences called permuted, a ,, *, (i = 1, ..., K; j = 1, ..., M9), each sequence a ,, * having a polynomial representation equal to a ,, * (x) = a, * (xe) modulo (x "+1), where - n is the product of the number M by the integer NO, - e ,, is a relatively prime number with n

- cI} is the quotient of a ,, * (x) by g, J (x), - the polynomial g ,, (x) is the generating polynomial of the smallest cyclic code of length NO containing the polynomial g1 (xeIJ) modulo (xN0 + 1), at least one permuted sequence aIJ * being different from the corresponding sequence a; 3 / it comprises a second operation of production of M1 redundant sequences whose polynomial representation is equal to E f ,, (x) c ,, (x), for j = 1, ..., M1, each polynomial f ,, (x) being a predetermined polynomial of degree at most equal to the degree of the polynomial g ,, (x) of the same indices i and j.

 We observe here that we say, then, that e belongs to the cycle of 2, modulo M.NO.

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 With these provisions, most of the columns of the table can be moved by permutation, on the one hand, and in this restricted choice, the minimum distance of the turbocode is more easily analyzable and therefore can be optimized, on the other hand.

 This second aspect of the invention has the same advantages as the first aspect.

 The inventors have observed that the implementation of the method of the present invention, in each of its aspects, as described above, had the advantage that any error estimation by the corresponding decoder converges. The case where the error estimation does not converge is therefore excluded by the implementation of the present invention.

 According to particular characteristics, during the first production operation, all the values of the exponents eIJ having the same value of the index j are identical.

 Thanks to these provisions, the coding method targeted by the present invention makes it possible to carry out all the interleaving operations that are fixed in the same way. It is therefore simple realization.

 According to particular characteristics, during the first production operation, all the exponent values eIJ are equal to a power of 2.

 With this arrangement, the polynomials gIJ are all identical.

 According to particular features, the coding method targeted by the present invention, as succinctly described above, comprises a transmission operation on the one hand of the sequences a, and, on the other hand, a subset of the data. other sequences.

 Thanks to these provisions, the efficiency of the process is increased.

 According to a third aspect, the present invention aims a coding device characterized in that it comprises a means of processing adapted to: 1 / take into account: a predetermined integer M1, equal to or greater than 2,

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- un nombre K, supérieur ou égal à 2, de séquences a, (i=1,...,K) de données binaires représentatives d'une grandeur physique, chaque séquence a, possédant : # une représentation polynomiale a,(x) multiple d'un polynôme g,(x) prédéterminé, et # un nombre de données binaires égal au produit d'un nombre entier M quelconque par l'entier NO, plus petit entier tel que le polynôme xN0+1 soit divisible par chacun des polynômes g,(x) ; 2/ production d'un nombre K*M1 de séquences dites permutées , aIJ*,

(i=1,...,K ; j=1,...,M9), chaque séquence a,* - étant obtenue par une permutation de la séquence a, correspondante, ladite permutation étant, dans une représentation où les données binaires de chaque séquence a, sont écrites, ligne par ligne, dans un tableau à NO colonnes et M lignes, la résultante d'un nombre quelconque de permutations dites élémentaires qui, chacune : # soit a la propriété de transformer le code cyclique de longueur NO et de polynôme générateur g,(x) en un code cyclique équivalent de polynôme générateur gIJ(x) pouvant être égal à g,(x), et agit par permutation sur les NO colonnes du tableau représentant a,, # soit est une permutation quelconque des symboles d'une colonne dudit tableau ; et - possédant, en conséquence, une représentation polynomiale a,,*(x) qui est égale à un produit polynomial c,,(x)g,,(x), - au moins une séquence permutée a,,* étant différente de la séquence a, correspondante, 3/ produire M1 séquences redondantes dont la représentation polynomiale est

égale à X f,,(x) c,!(x), pour/=1 M1, chaque polynôme f,,(x) étant un polynôme de degré au plus égal au degré du polynôme g,,(x) de mêmes indices i etj.

a number K, greater than or equal to 2, of sequences a, (i = 1, ..., K) of binary data representative of a physical quantity, each sequence a, having: # a polynomial representation a, (x ) multiple of a predetermined polynomial g, (x), and # a number of binary data equal to the product of any integer M by the integer NO, smaller integer such that the polynomial xN0 + 1 is divisible by each polynomials g, (x); 2 / production of a number K * M1 of sequences called permuted, aIJ *,

(i = 1, ..., K; j = 1, ..., M9), each sequence a, * - being obtained by a permutation of the sequence a, corresponding, said permutation being, in a representation where the data bits of each sequence a, are written, line by line, in an array with NO columns and M rows, the resultant of any number of so-called elementary permutations which, each: # has the property of transforming the cyclic code of length NO and of generator polynomial g, (x) into an equivalent cyclic code of generator polynomial gIJ (x) which may be equal to g, (x), and acts by permutation on the NO columns of the array representing a ,, # is a permutation any symbols of a column of said array; and - having, accordingly, a polynomial representation a ,, * (x) which is equal to a polynomial product c ,, (x) g ,, (x), - at least one permuted sequence a ,, * being different from the sequence a, corresponding, 3 / produce M1 redundant sequences whose polynomial representation is

equals X f ,, (x) c,! (x), for / = 1 M1, each polynomial f ,, (x) being a polynomial of degree at most equal to the degree of the polynomial g ,, (x) of the same indices i andj.

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- un nombre K, supérieur ou égal à 2, de séquences a, (i=1,...,K) de données binaires représentatives d'une grandeur physique, chaque séquence a, possédant : # une représentation polynomiale a,(x) multiple d'un polynôme g,(x) prédéterminé et sans facteurs polynomiaux multiples, et # un nombre de données binaires égal au produit d'un nombre entier impair M quelconque par l'entier NO, plus petit entier tel que le polynôme xN0+1 soit divisible par chacun des polynômes g,(x) ;

2/ produire un nombre K*M1 de séquences dites permutées , a,,*, (i=1,...,K ; j=1,...,M1), chaque séquence a,J* possédant une représentation polynomiale égale à a/fx)=a/*(xe'1) modulo (x"+1), où - n est le produit du nombre M par l'entier NO, - EIJ est un nombre relativement premier avec n

- c,, est le quotient de a/(x) par g,,(x), - le polynôme g,,(x) est le polynôme générateur du plus petit code cyclique de longueur NO contenant le polynôme gI(xeij) modulo

(,/J +1 ), au moins une séquence permutée aIJ* étant différente de la séquence a, correspondante ; 3/ produire M1 séquences redondantes dont la représentation polynomiale est

égale à E f,,(x) c,J(x), pour j=1 ,...,M1, chaque polynôme "lx) étant un polynôme prédéterminé de degré au plus égal au degré du polynôme gIJ(x) de mêmes indices /et j. According to a fourth aspect, the present invention aims a coding device characterized in that it comprises a processing means adapted to: 1 / take into account: a predetermined integer M1, equal to or greater than 2,

a number K, greater than or equal to 2, of sequences a, (i = 1, ..., K) of binary data representative of a physical quantity, each sequence a, having: # a polynomial representation a, (x ) multiple of a predetermined polynomial g, (x) and without multiple polynomial factors, and # a number of binary data equal to the product of an odd integer M by the integer NO, smaller integer such that the polynomial xN0 +1 is divisible by each of the polynomials g, (x);

2 / to produce a number K * M1 of sequences called permuted, a ,, *, (i = 1, ..., K; j = 1, ..., M1), each sequence a, J * having a polynomial representation equal to a / fx) = a / * (xe'1) modulo (x "+1), where - n is the product of the number M by the integer NO, - EIJ is a relatively prime number with n

- c ,, is the quotient of a / (x) by g ,, (x), - the polynomial g ,, (x) is the generating polynomial of the smallest cyclic code of length NO containing the polynomial gI (xeij) modulo

(, / J +1), at least one permuted sequence aIJ * being different from the corresponding sequence a; 3 / produce M1 redundant sequences whose polynomial representation is

equal to E f ,, (x) c, J (x), for j = 1, ..., M1, each polynomial "1x) being a predetermined polynomial of degree at most equal to the degree of the polynomial gIJ (x) of same indices / and j.

 According to a fifth aspect, the present invention aims a decoding method characterized in that: 1 / it takes into account:

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 a predetermined integer M1, equal to or greater than 2, a number K, greater than or equal to 2, of sequences a, (/=1, ..., K) of data representative of a physical quantity, each sequence has , having: # a polynomial representation a, (x) multiple of a predetermined polynomial g, (x), and # a number of binary data equal to the product of any integer M by the integer NO, smaller integer such that the polynomial xN0 + 1 is divisible by each of the polynomials g, (x); 2 / it comprises a parallel turbodecoding operation of K symbol sequences implementing the divisor polynomials g ,, (x).

3 / it comprises, for each a ,, M1 operations of permutation, of which at least one is not the identity, each permutation being, in a representation where the binary data of each sequence a, are written line by line, in a table with NO columns and M rows, the resultant of any number of so-called elementary permutations, each of which: # has the property of transforming the cyclic code of length NO and of generator polynomial g, (x) into a code cyclic equivalent of generator polynomial g ,, (x) being able to be equal to g, (x), and acts by permutation on the NO columns of the array representing a ,, # is any permutation of the symbols of a column of said array.

- un nombre K, supérieur ou égal à 2, de séquences a, (i=1,...,K) de données représentatives d'une grandeur physique, chaque séquence a, possédant : According to a sixth aspect, the present invention aims a decoding method characterized in that: 1 / it takes into account: a predetermined integer M1, equal to or greater than 2,

a number K, greater than or equal to 2, of sequences a, (i = 1, ..., K) of data representative of a physical quantity, each sequence a, having:

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permutation produisant des séquences dites permutées , a,,*, (i=1,...,K; ;'=1,...,M7), chaque séquence permutée a,,* possédant une représentation polynomiale égale à alJ *(x)=a,*() modulo (x"+1), où : - n est le produit du nombre M par l'entier NO, eIJ est un nombre relativement premier avec n - cI} est le quotient de aIJ*(x) par g,,(x), - le polynôme g,,(x) est le polynôme générateur du plus petit code cyclique de longueur NO contenant le polynôme gI(xeIJ) modulo

(>1' +1 ), au moins une séquence permutée a,,* étant différente de la séquence a, correspondante. # a polynomial representation a, (x) multiple of a predetermined polynomial g, (x) and without multiple polynomial factors, and # a number of binary data equal to the product of an odd integer M by the integer NO, smaller integer such that the polynomial xN0 + 1 is divisible by each of the polynomials g, (x); 2 / it comprises a parallel turbodecoding operation of K symbol sequences implementing the divide polynomials g ,, (x), 3 / said parallel turbodecoding operation comprising a

permutation producing sequences called permuted, a ,, *, (i = 1, ..., K;; '= 1, ..., M7), each permuted sequence a ,, * having a polynomial representation equal to alJ * (x) = a, * () modulo (x "+1), where: - n is the product of the number M by the integer NO, eIJ is a relatively prime number with n - cI} is the quotient of aIJ * (x) by g ,, (x), - the polynomial g ,, (x) is the generator polynomial of the smallest cyclic code of length NO containing the polynomial gI (xeIJ) modulo

(> 1 '+1), at least one permuted sequence a ,, * being different from the corresponding sequence a.

 According to a seventh aspect, the present invention aims a decoding device characterized in that it comprises a suitable processing means: 1 / to take into account: a predetermined integer M1, equal to or greater than 2, a number K, greater than or equal to 2, of sequences a, (i = 1, ..., K) of data representative of a physical quantity, each sequence a, having: # a polynomial representation a, (x) multiple of a polynomial g, (x) predetermined, and # a number of binary data equal to the product of any integer M by the integer NO, smaller

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 integer such that the polynomial xN0 + 1 is divisible by each of the polynomials g, (x); 2 / to perform a parallel turbodecoding operation of K symbol sequences implementing the divide polynomials g ,, (x).

3 / to perform, for each a ,, M1 permutation operations, at least one of which is not the identity, each permutation being, in a representation where the binary data of each sequence a, are written, line by line, in a table with NO columns and M rows, the resultant of any number of so-called elementary permutations, each of which: # has the property of transforming the cyclic code of length NO and of generator polynomial g, (x) into a code cyclic equivalent of generator polynomial gij (x) may be equal to g, (x), and acts by permutation on the NO columns of the array representing a ,, # is any permutation of the symbols of a column of said array.

- un nombre K, supérieur ou égal à 2, de séquences a, (i=1,...,K) de données représentatives d'une grandeur physique, chaque séquence a, possédant : # une représentation polynomiale a,(x) multiple d'un polynôme g,(x) prédéterminé et sans facteurs polynomiaux multiples, et . un nombre de données binaires égal au produit d'un nombre entier impair M quelconque par l'entier NO, plus petit entier tel que le polynôme xN0+1 soit divisible par chacun des polynômes g,(x) ; 2/ à effectuer une opération de turbodécodage parallèle de K séquences de symboles mettant en #uvre les polynômes diviseurs g,,(x), According to an eighth aspect, the present invention aims a decoding device characterized in that it comprises a suitable processing means: 1 / to take into account: a predetermined integer M1, equal to or greater than 2,

a number K, greater than or equal to 2, of sequences a, (i = 1, ..., K) of data representative of a physical quantity, each sequence a, having: # a polynomial representation a, (x) multiple of a predetermined polynomial g, (x) and without multiple polynomial factors, and. a number of binary data equal to the product of any odd integer M by the integer NO, smaller integer such that the polynomial xN0 + 1 is divisible by each of the polynomials g, (x); 2 / performing a parallel turbodecoding operation of K symbol sequences implementing the divide polynomials g ,, (x),

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permutées , a,,*, (i=1 ,...,K,. j=1,...,Ml ), chaque séquence permutée a,l* possédant une représentation polynomiale égale à aIJ*(x)=a*(xe'1) modulo (x"+1), où : - n est le produit du nombre M par l'entier NO, - e,, est un nombre relativement premier avec n

- ci, est le quotient de a;,*(x) par g,,(x), - le polynôme gIJ(x) est le polynôme générateur du plus petit code cyclique de longueur NO contenant le polynôme gI(xeij) modulo

(,,(J +1 ), au moins une séquence permutée aIJ* étant différente de la séquence a, correspondante. 3 / to perform a permutation operation producing so-called sequences

permuted, a ,, *, (i = 1, ..., K, j = 1, ..., M1), each permuted sequence a, l * having a polynomial representation equal to aIJ * (x) = a * (xe'1) modulo (x "+1), where: - n is the product of the number M by the integer NO, - e ,, is a relatively prime number with n

- ci, is the quotient of a;, * (x) by g ,, (x), - the polynomial gIJ (x) is the generating polynomial of the smallest cyclic code of length NO containing the polynomial gI (xeij) modulo

(,, (+1), at least one permuted sequence aIJ * being different from the corresponding sequence a.

 The invention also relates to: a means for storing information readable by a computer or a microprocessor retaining instructions of a computer program, characterized in that it allows the implementation of the method of the invention such that briefly described above, and a means for storing removable information, partially or totally, readable by a computer or a microprocessor retaining instructions of a computer program, characterized in that it allows the implementation of the method of the invention as succinctly set forth above.

 The invention also relates to: a signal processing device representative of speech, which comprises a device as briefly described above, a data transmission device comprising a transmitter adapted to implement a transmission protocol by packets, which comprises a device as briefly described above, - a data transmission device comprising a transmitter adapted to implement the ATM packet transmission protocol (asynchronous transfer mode, Asynchronous Transfer Mode), which comprises a device as briefly described above,

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 a data transmission device comprising a transmitter adapted to implement the packet transmission protocol, on a network of the ETHERNET type, a network station, which comprises a device as briefly described below; above, - a data transmission device comprising an emitter emitting on a non-wire channel, which comprises a device as briefly described above, and a signal sequence processing device representative of at most one thousand binary data, which comprises a device as succinctly set forth above.

 These coding and decoding devices, these coding and decoding methods and the signal processing, data transmission, sequence processing and network devices having the same particular characteristics and the same advantages as the coding method such as: as succinctly set forth above, these particular features and advantages are not recalled here.

 The invention will be better understood on reading the description which follows, given with reference to the accompanying drawings, in which: FIG. 1 is a diagrammatic representation of an electronic device incorporating an encoder according to a first embodiment of the present invention; FIG. 2 diagrammatically represents an operating flow chart of an encoder according to the first embodiment of the present invention, as illustrated in FIG. 1; FIG. 3 diagrammatically represents a flowchart describing the steps for determining an interleaver implemented in the device illustrated in FIG. 1; FIG. 4 diagrammatically represents an encoder according to the second embodiment of the present invention; FIG. 5 schematically represents the general form of interleavers acting on several symbol sequences to be coded;

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 FIG. 6 represents a performance curve of particular examples of methods and devices according to the second embodiment of the present invention; FIG. 7 is a schematic representation of an electronic device incorporating an encoder according to a second embodiment of FIG. the present invention; FIG. 8 schematically represents an operating flow chart of an encoder according to the second embodiment of the present invention, as illustrated in FIG. 7; FIG. 9 represents, schematically, a decoding device targeted by the present invention.

 In the following description, the first control sequence will always be obtained from non-interlaced information sequences, although the scope of the invention also extends to general cases.

 The description of embodiments of the invention is, below, divided into two parts, respectively dedicated to the case in which a single sequence of symbols is coded and to the case in which at least two sequences of symbols are simultaneously coded.

I - FIRST EMBODIMENT
In the following description, "data" is understood to be both representative symbols of information and additional or redundant symbols.

 Before beginning the description of a particular embodiment, the mathematical foundations of its implementation are given below.

par les divisions b(x) = a(x).hl(x)lg(x) et c(x) = a *(x).h2(x)/g(x), ne présentent aucun reste.

A cet effet, g(x) = 1 + Zl=1 a m-1 gox + xm étant un polynôme de degré m prédéterminé, on recherche le plus petit nombre NO tel que g(x) divise In the invention, g (x), h1 (x) and h2 (x) being predetermined, it is recalled that it is desired that the sequences b and c, respectively defined

by the divisions b (x) = a (x), h1 (x) 1g (x) and c (x) = a * (x) .h2 (x) / g (x), have no remainder.

For this purpose, g (x) = 1 + Z1 = 1a m-1, where x is a polynomial of predetermined degree m, we search for the smallest number NO such that g (x) divides

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 the polynomial xN0 - 1. We know that this number exists. For example for g (x) = 1 + x + x3, NO = 7.

 Then, by choosing any number M, we choose a sequence length a equal to M.NO, which amounts to determining the length (that is to say the number of binary data) of the sequence u incorporated into the sequence a as being equal to M.NO minus the degree of g (x).

 Thus, to form the sequence a, juxtapose to the sequence u formed of k binary data u, to be transmitted, a number of additional binary data equal to the degree of the polynomial g (x), the added data ensuring the absence of a remainder in the division of a (x) by g (x).

 We recall that the division made here is, modulo 2, on the coefficients of the increasing powers of a (x).

ce qui s'écrit aussi : (1, 0, 0, 1, 0, 0, 0, 0, 0) = (1, 1, 0, 1) x (1, 1, 1, 1, 0, 1) + (0, 0, 0, 0, 0, 0, 0, 0, 1), soit encore (1, 0, 0, 1, 0, 0, 0, 0, 1) = (1, 1, 0, 1) x (1, 1, 1, 1, 0, 1), en ajoutant, terme à terme, la séquence de reste (0, 0, 0, 0, 0, 0, 0, 0, 1) à la séquence u d'abord complétée par m "0". By way of example, if the sequence u is the sequence (1, 0, 0, 1, 0, 0), and the sequence g is the sequence (1, 1, 0, 1), the division is written as follows:

what is also written: (1, 0, 0, 1, 0, 0, 0, 0, 0) = (1, 1, 0, 1) x (1, 1, 1, 1, 0, 1) + (0, 0, 0, 0, 0, 0, 0, 0, 1), that is to say (1, 0, 0, 1, 0, 0, 0, 0, 1) = (1, 1, 0, 1) x (1, 1, 1, 1, 0, 1), adding, term by term, the remainder sequence (0, 0, 0, 0, 0, 0, 0, 1) to the sequence u first completed by m "0".

 Thus, by substituting for the sequence u = (1, 0, 0, 1, 0, 0), the sequence a = (1, 0, 0, 1, 0, 0, 0, 0, 1), formed by this addition, and whose

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séquence g = (1, 1, 0, 1), et, par conséquent de a(x).h1(x) par g(x), quelle que soit la séquence hi associée au polynôme hi(x), ce qui fournit la définition de la séquence b par b(x) = a(x).h,(x)lg(x). first binary data are all the binary data of the sequence u, we guarantee the divisibility of the polynomial a (x) by the polynomial g (x) associated with the

sequence g = (1, 1, 0, 1), and therefore of a (x) .h1 (x) by g (x), whatever the sequence hi associated with the polynomial hi (x), which provides the definition of the sequence b by b (x) = a (x) .h, (x) lg (x).

 To determine the sequence a * (x), which has, after permutation, the same binary data as the sequence a, but in a different order, we choose an interleaver whose representation can be given in the following way: the binary data of the sequence a being classified in an array of NO columns and M lines, one carries out on these data at least one permutation in a set of permutations comprising, on the one hand, the automorphisms of the binary cyclic code of length NO and generator polynomial g (x), permutating between them at least two of the NO columns of the array and, on the other hand, permutations working only on data of the same column and permutating between them at least two of said data, and only one or more permutations of this set.

 In fact, the inventors have discovered that only the permutations that can be so represented guarantee that for every polynomial a (x) whose division by g (x) has no remainder, the permuted polynomial a * (x) has a division by g (x) which has no remainder.

 In such a succession, one can, for example in the case where NO = 7 and g (x) = 1 + x + x 3, successively find: - a permutation of the binary data of the first column, - a permutation of the binary data of the third column, - the replacement of the second column by the fourth, the replacement of the fourth column by the second, the replacement of the fifth column by the sixth and the replacement of the sixth column by the fifth.

 With respect to automorphism, by calling Cg the binary cyclic code of length NO and of generator polynomial g (x), that is to say the set of multiples of g (x), modulo xN0-1, we consider the permutations

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 coordinates of this code which transform any word of this code into another word of this code. The set of coordinate permutations that have this property has a group structure and is called the Cg automorphism group.

 For more details, the reader will be able to refer to the work of Mrs. F. J. MAC WILLIAMS and Mr. N. J. A. SLOANE, "The theory of error-correcting codes" published by the publisher North-Holland in 1977.

 Among all these permutations, the inventors have selected the following permutations, which have the advantage of being a small family of which all members can be tested to choose the most efficient permutation.

celui-ci est défini par a*(x) = a(xe), ainsi, si a=(ao, a, a2, aM NO-1), la première donnée binaire de a* est ao, la seconde af, la troisième a2f, f étant l'inverse de e, modulo M.NO, et les multiples de f étant, eux-mêmes calculés modulo M. N0. As mentioned above, we choose M odd and g (x) such that the corresponding NO number is also odd. By writing the successive powers of 2 modulo M.NO, we obtain what is called the cycle of 2, modulo M.NO. In this cycle, by choosing any term e, we carry out the following permutation: the polynomial a (x) giving, after permutation, the polynomial a * (x),

this is defined by a * (x) = a (xe), so, if a = (ao, a, a2, aM NO-1), the first binary of a * is ao, the second af, the third a2f, f being the inverse of e, modulo M.NO, and the multiples of f being, themselves calculated modulo M. N0.

 For example, by taking g (x) = 1 + x + x3, and hence NO = 7, and choosing M = 5, we have M. NO = 35. The cycle of 2 is then written as: [1, 2, 4, 8, 16, 32, 29, 23, 11, 22, 9, 18].

 Taking, for example, e = 28 = 11, f will be worth 16 and the sequence a * begins with the binary data: ao, a16, a32, a13, a29, a10, etc.

 These permutations described above and representable by a * (x) = a (xe) where e is in the cycle of 2 modulo M.NO, a (xe) being taken modulo xM N0 -1, form a small family of which all members can be tested to choose the best performer.

 The selection logic is as follows: we first choose g (x) of degree m not divisible by a square polynomial. This choice sets the value of NO

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spécifier a*(x) = a(xe) modulo )('vfNO-1~1 à partir de a(x) et on effectue diverses opérations de test sur le turbocode associé à l'entrelaceur ainsi défini. as the smallest integer such that g (x) divides xN0-1. Moreover, the fact that the polynomial g (x) is not divisible by a square polynomial implies that NO is an odd number. We then choose hi (x) and h2 (x) of any degree but preferably at most equal to the degree m of g (x) because the maximum of the degrees of these three polynomials g (x), hi (x) and h2 (x ) is a decisive element in the complexity of the decoder. Then choose an odd integer M and calculate the cycle of 2, modulo M.NO. We then choose an element e in this cycle of 2 for

specify a * (x) = a (xe) modulo) ('vfNO-1 ~ 1 from a (x) and perform various test operations on the turbocode associated with the interleaver thus defined.

Choisissons aussi hi(x) = 1 + x + X2 + x3, h2(x) = 1 + X2 + x3 et M = 21 ceci entraîne M.NO =147 et permet de calculer le cycle de deux modulo 147 comme étant {1, 2, 4, 8, 16, 32,64, 128,109, 71, 142, 137, 127, 107,67, 134, 121, 95, 43, 86, 25, 50,100, 53,106, 65,130, 113,79, 11,22, 44,88, 29,58, 116,85, 23, 46, 92,37, 74}. Take for example g (x) = 1 + x + x3, this imposes NO = 7.

Let us also choose hi (x) = 1 + x + X2 + x3, h2 (x) = 1 + X2 + x3 and M = 21 this gives M.NO = 147 and allows the cycle of two modulo 147 to be calculated as {1 , 2, 4, 8, 16, 32, 64, 128, 109, 71, 142, 137, 127, 107, 67, 134, 121, 95, 43, 86, 25, 50, 100, 53, 106, 65, 130, 113, 79, 11. , 22, 44.88, 29.58, 116.85, 23, 46, 92.37, 74}.

(a, b, cl de poids bzz 24, les a(x) de poids 4 correspondent alors à une séquence codée v= (a, b, cl de poids bzz 26, les a(x) de poids 5 correspondent alors à une séquence codée v= (a, b, c) de poids 30... By successively testing the polynomials a (x) divisible by g (x) of weight equal to 2.3, 4 and 5, we conclude that the choice e = 25 is "promising" because the a (x) of weight 2 correspond then at a coded sequence v = (a, b, c) of weight> 26, the a (x) of weight 3 then correspond to a coded sequence v =

(a, b, cl of weight bzz 24, the a (x) of weight 4 then corresponds to a coded sequence v = (a, b, cl of weight bzz 26, the a (x) of weight 5 then correspond to a coded sequence v = (a, b, c) of weight 30 ...

 This seems to indicate a minimum distance equal to 24, which is the best value that can be obtained according to the method explained above for NO = 7 and M = 21 with g (x), h1 (x) and h2 (x) as stated above.

 Another possible choice is g (x) = 1 + x + x4 which imposes NO = 15.

Let us also choose h1 (x) = 1 + x + x2 + x4, h2 (x) = 1 + x3 + x4 and M = 27. This results in M.NO = 405 and calculates the cycle of 2 modulo 405 as { 1,2,4,8,16,304,203}. It includes 108 numbers.

 Working by successive elimination, we conclude that the choices e = 151, e = 362 and e = 233 are particularly promising.

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 In particular for e = 151, the inventors tested the polynomials a (x) divisible by g (x) and of weight equal successively to 2,3, 4,5, 6 and 7 and such that, if this weight is greater or equal to 5, then the weight of a (x), denoted W (a (x)), is equal to the weight of a (x) modulo x15 + 1.

When the weight of a (x) is W (a (x)), the corresponding minimum weight of W (v) is indicated in the table:

<Tb>
<tb> W (a (x)) <SEP> W (v) <SEP>#
<tb> 2 <SEP> 54
<tb> 3 <SEP> 42
<tb> 4 <SEP> 44
<tb> 5 <SEP> 48
<tb> 6 <SEP> 54
<tb> 7 <SEP> 54
<Tb>

In the same way and under the same conditions, for e = 362, when the weight of a (x) is W (a (x)), the corresponding minimum weight of W (v) is indicated in the table:

<Tb>
<tb> W (a (x)) <SEP> W (v) <SEP>#
<tb> 2 <SEP> 54
<tb> 3 <SEP> 42
<tb> 4 <SEP> 42
<tb> 5 <SEP> 50
<tb> 6 <SEP> 56
<tb> 7 <SEP> 54
<Tb>

According to the invention, the numbers e, not congruent to 1, modulo NO, can be particularly used.

 The description of a particular embodiment of the present invention will now be continued with reference to FIGS. 1 to 3.

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 FIG. 1 schematically illustrates the constitution of a network station or computer coding station, in the form of a block diagram. This station comprises a keyboard 111, a screen 109, an external information source 110, a radio transmitter 106, jointly connected to an input / output port 103 of a processing card 101.

The processing card 101 comprises, interconnected by an address and data bus 102: a central processing unit 100; a RAM 104; a ROM 105; the input / output port 103;
Each of the elements illustrated in Figure 1 is well known to those skilled in the field of microcomputers and transmission systems and, more generally, information processing systems. These common elements are therefore not described here. It is observed, however, that: the information source 110 is, for example, an interface device, a sensor, a demodulator, an external memory or another information processing system (not shown), and is preferably adapted to provide signal sequences representative of speech, service messages or multimedia data, in the form of binary data sequences, - the radio transmitter 106 is adapted to implement a packet transmission protocol on a channel not wired, and to transmit these packets on such a channel.

 It is further observed that the word "register" used in the description designates, in each of the memories 104 and 105, both a memory area of low capacity (a few binary data) and a memory area of large capacity (allowing store an entire program).

 The RAM 104 stores data, variables and intermediate processing results in memory registers carrying, in the description, the same names as the data whose values they retain. RAM 104 comprises in particular:

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- un registre "resfe intermédiaire" dans lequel sont conservés successivement les restes intermédiaires de la division, registre utilisé pour construire la séquence a, à partir de la séquence u,

- un registre "reste finaP' dans lequel sont conservées des données binaires complémentaires, sous forme d'une séquence, - un registre "données-permutées" dans lequel sont conservées, dans l'ordre de leur arrivée sur le bus 102, les données binaires permutées, comme décrit en regard de la figure 2, sous forme d'une séquence a*, et - un registre "a, b, c" dans lequel sont conservées, dans l'ordre de leur détermination par l'unité centrale 100, les données binaires de séquence en cours de traitement. a "primary-data" register in which, in the order of their arrival on the bus 102, the binary data coming from the information source 110 are stored in the form of a sequence u, which is then completed to form a sequence a, - a register "nb ~ data" which keeps an integer corresponding to the number of binary data nm in the register "data ~ binary",

a register "intermediate resf" in which are conserved successively the intermediate remains of the division, register used to construct the sequence a, from the sequence u,

a register "remains fina" in which are kept complementary binary data, in the form of a sequence, - a "data-permuted" register in which are kept, in the order of their arrival on the bus 102, the data binary permuted, as described with reference to FIG. 2, in the form of a sequence a *, and - a register "a, b, c" in which are conserved, in the order of their determination by the central unit 100 , the binary sequence data being processed.

- la séquence /111 dans un registre "/1/', - la séquence h2, dans un registre "h2", - la valeur de N0, dans un registre "NO", - la valeur de M, dans un registre "M", et - le tableau définissant l'entrelaceur, dans un registre "entrelaceur". The read-only memory 105 is adapted to keep, in registers which, for convenience, have the same names as the data they retain: the operating program of the central processing unit 100, in a "program" register, the sequence g, in a register "g", the degree m of g (x), in a register "degree"

the sequence / 111 in a register "/ 1 /", - the sequence h2, in a register "h2", - the value of N0, in a register "NO", - the value of M, in a register "M ", and - the array defining the interleaver, in an" interleaver "register.

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 The central processing unit 100 is adapted to implement the flowchart described in FIG. 2.

 In FIG. 2, which represents the operation of an encoder as illustrated in FIG. 1, it is observed that after an initialization operation 300, during which the registers of the random access memory 104 are initialized (nb ~ data = "0"), during an operation 301, the central unit 100 waits to receive, then receives a binary data to be transmitted, places it in random access memory 104, in the "primary data" register and increments the counter "nb data".

 Then, during a test 302, the central unit 100 determines whether the whole number stored in the register "nb ~ data" is equal to the product M.NO to which is subtracted the degree of g (x), M, NO and the degree m of g (x) being values stored in read-only memory 105.

#uvre, à cet effet, le registre "reste~intermédiaire", le reste de cette division est mis en mémoire dans le registre "reste~finaP'. Ensuite, au cours d'une opération 304, les données binaires

conservées dans le registre "reste fnaP' sont juxtaposées à la fin de la séquence u pour former la séquence a. Les données binaires de la séquence a sont mises en mémoire dans le registre "a, b, c". When the result of the test 302 is negative, the operation 301 is repeated. When the result of the test 302 is positive, during an operation 303, the division of the polynomial u (x) associated with the binary data sequence stored in the "primary data" register by the polynomial g (x) is carried out, until the last term (of the highest degree) of u (x),

For this purpose, the register "remains intermediate", the remainder of this division is stored in the register "remains ~ finaP" Then, during an operation 304, the binary data

stored in the register "remain fnaP" are juxtaposed at the end of the sequence u to form the sequence A. The binary data of the sequence a are stored in the register "a, b, c".

 Then, during an operation 305, the division performed during the operation 303 is continued, with the additional data added during the operation 304 and the sequence b is completed in the register "a, b, c ".

 Then, during an operation 306, the binary data of the sequence a are successively read in the register "a, b, c", in the order described by the "interleaver" table stored in the read-only memory 105.

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dans le registre "données permutées" de la mémoire vive 104. data resulting from this reading are stored in memory

in the "swapped data" register of the random access memory 104.

 Then, during an operation 307, the division of the polynomial a * (x) associated with the permuted bit data sequence stored in the register "data ~ permuted" by the polynomial g (x) is performed, by setting # for this purpose, the register "remains ~ intermediate". The result of this division is stored in the register "a, b, ç", and corresponds to the binary data of the sequence ç.

 During an operation 308, the sequences b and c are determined by producing the product of the polynomials associated with the sequences b and c kept in the register "a, b, c" of the random access memory 104, respectively by the polynomials h ( x) and h2 (x).

 It is observed that, thanks to the invention, we gain memory elements by dividing by g (x) before the multiplication by hi (x) or h2 (x).

 During an operation 309, the sequences a, b, and c are emitted using, for this purpose, the transmitter 106. Then, the registers of the memory 104 are initialized again, in particular the counter Nb ~ data. is reset to "0" and operation 301 is repeated.

 It is observed here that, alternatively, during the operation 309, the sequence a is transmitted in its entirety, but only a subset, for example every other data item, of each of the sequences b and c is emitted.

This variant is known to those skilled in the art under the name of punching.

 With regard to the decoding, it is observed that by knowing the polynomials g (x), h1 (x), h2 (x) and the interleaver which, from the sequence a provide the permuted sequence a *, the One skilled in the art knows, without any technical problem, making the decoder suitable for decoding and error correction affecting the sequence triplet (a, b, c) by using the interleaver considered above and possibly the corresponding de-interleaver.

 For this purpose he may refer to: - the article by MM. L. R. BAHL, J. COCKE, F. JELINEK and J.

RAVIV entitled "Optimal decoding of linear codes for minimizing symbol error

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 rate ", published in the journal IEEE Transactions on Information Theory, in March 1974. - in the article by J. HAGENAUER, E. OFFER and L. PAPKE entitled" Iterative decoding of binary block and convolutional codes "published in the IEEE Reviews Transactions on Information Theory, in March 1996 - in the article by J. HAGENAUER and P. HOEHER entitled "A Viterbi algorithm with soft decision outputs and its applications", published with the IEEE conference proceedings GLOBECOM, pages 1680-1686, in November 1989. - in the article by J. HAGENAUER, P. ROBERTSON and L.

PAPKE entitled "Iterative (turbo) decoding of systematic convolutional codes with MAP and SOVA algorithms", published by the magazine Informationstechnische Gesellschaft (ITG) Fachbericht, pages 21-29, October 1994; - in the article of MM. C. BERROU, S. EVANO and G. BATTAIL, entitled "Turbo-block-codes" and published with the minutes of the "turbo coding" seminar organized by the Lund Institute of Technology (Sweden) (Department of Electronics applied in August 1996.

lequel des registres "NO", "M", "entrelaceur "d", "dmax", "e" et 'j" se trouvent, en mémoire vive. FIG. 3 shows the steps of an algorithm for determining the value of e specifying the interleaver to be used. These steps can be performed by a computer of known type (not shown), in

which registers "NO", "M", "interleaver" d "," dmax "," e "and" j "are in RAM.

During an operation 501, g (x) = 1 + 1; 1 to m-1 9 + x 'being the polynomial of predetermined degree m corresponding to the sequence g, the smallest integer strictly positive NO such that g (x) divides the polynomial xN0 - 1. We know that this number exists. For example, for g (x) = 1 + x + x3, NO = 7. For this purpose, the divisions of the polynomials x '- 1 are successively carried out by g (x) starting with a value of i equal to the degree m of g (x) by progressively incrementing i, with an incrementation step of 1, until the remainder of the division is zero, modulo 2. When the remainder is zero, the value of i is set in the register NO . It is recalled that the division

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 done here is, modulo 2, on the coefficients of the increasing powers of / -7.

 Then, by choosing an odd number M, such that the product M.NO is greater than or equal to the number of binary data u, which must be transmitted in the same frame, added to the degree m of g (x), during of an operation 502, a sequence length equal to M.NO is chosen. which amounts to determining the length (i.e., the number of binary data) of the sequence u incorporated in the sequence a as being equal to M.NO minus the degree m of g (x).

 Then, during operations 503 to 509, the central unit 100 determines whether the interleaver associated with e is to be taken into account, which means that there is no low order sequence a for which the sequence v = (a, b, c) also has a low weight.

 In the embodiment described and shown, the determination of a * will consist of replacing a = (ao, a1, ...) by a * = (ao, af, a2f, ...) where the multiples of f are calculated modulo M.NO. When f is equal to a power of 2 different from 1, modulo M.NO, this permutation is of the type announced.

It can, indeed, be represented by a permutation which swaps binary data only inside each column of the array, followed, when f is equal to a power of 2 different from 1, modulo NO, of one permutation of at least two of the columns together, the latter permutation being an automorphism of the binary cyclic code of length NO and of generator polynomial g (x). When f is equal to 1, modulo N0, this permutation on the columns is the "trivial" permutation or "identity" permutation, that is, the one that maintains the position of the columns in the array.

 For this purpose, in this particular embodiment of the present invention, during the operation 503, the central unit 100 determines the successive powers of 2 modulo M. N0, to obtain what is called the cycle of 2 , modulo M.NO, this cycle being completed as soon as one of the powers of 2 is equal to 1, modulo M.NO. The number of terms j of this cycle is stored in the register "j".

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 Then, during the operation 504, the intermediate values / and dmax stored in the registers "@" and "dmax" are initialized respectively at the value "1" and at the value "0".

 Then, during an operation 505, the value of / is incremented by "1" and the second value of the cycle of 2, modulo M.NO is taken.

si a=(ao, a,, a2, ..., aMNO-r), la première donnée binaire de a* est ao, la seconde af, la troisième a2f, ..., comme exposé supra, l'indice étant calculé modulo M. NO). Then, during an operation 506, if this value is not equal to 1 modulo M.NO, we determine the weight of the sequence v = (a, b, c) for the low-weight sequences a, with the permutation defined by a * (x) = a (xe) (thus,

if a = (ao, a ,, a2, ..., aMNO-r), the first binary of a * is ao, the second af, the third a2f, ..., as explained above, the index being calculated modulo M. NO).

 For this purpose, since the distance between two sequences is the weight (that is to say the number of non-zero binary data) of the sequence constituted by the difference of the binary data homologous to these sequences, it is limited to the analysis of the distance of the sequences with the null sequence, one lists the polynomials a (x) by increasing weight, one measures the sum of the weights of the sequences of the same triplet (a, b, c) and one seeks the minimum weight for e given, for the low order sequences a, and, once all these minimum weights determined for e in the cycle of 2, the value of e which corresponds to the highest weight.

 The distance is then stored in the register "d" of the RAM 104. Then, if, during a test 507, the value stored in the register "d" is greater than the value kept in the register "dmax" , then during the operation 508, the value of the register "dmax" is modified to take the value d and the value of the eighth element of the cycle considered is stored in the register "e".

Following the operation 508 or, when the result of the test 507 is negative, as long as the value of / is less than j, test 509, the operation 505 is repeated.

The "entrelaceue" table is then constituted as follows:

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a*(x) = a(xe), ainsi, si a=(ao, ah a2, ..., aM NO-1) , la première donnée binaire de a* est ao, la seconde af, la troisième a2f, comme exposé supra, l'indice étant calculé modulo M.NO.

a * (x) = a (xe), so, if a = (ao, ah a2, ..., aM NO-1), the first binary of a * is ao, the second af, the third a2f, as explained above, the index being calculated modulo M.NO.

- a(x) et b(x) = a(x).h(x)lg(x) sont définis comme ci-dessus, - étant donné un polynôme g2(x) choisi tel que le plus petit entier N2 tel que g2(x) divise le polynôme xN2 -1 soit égal au plus petit entier NO tel que g(x) divise le polynôme xN0 - 1, on choisit une permutation P qui transforme tout mot du code cyclique binaire de longueur NO et de polynôme générateur g(x) en un mot du code cyclique binaire de longueur N2 et de polynôme générateur g2(x). On note qu'une telle permutation n'existe que pour les polynômes g2(x) engendrant des codes cycliques équivalent à Cg. Cette vérification est bien connue de l'homme du métier et nous renvoyons pour cela à la page 234 du livre de Mme F. J. MAC WILLIAMS et M. N. J.A. SLOANE mentionné ci-dessus ; - selon l'invention, la permutation qui, à partir de la séquence a, associée au polynôme a(x) divisible par g(x), produit la séquence a**, associée au polynôme a**(x), divisible par g2(x) est alors produite par une permutation quelconque produisant à partir de a(x) une première séquence a*(x) divisible par g(x) comme expliqué ci-dessus, suivie de la permutation P que nous venons d'introduire et qui agit sur les colonnes du tableau à M lignes et NO colonnes contenant tout d'abord a et ensuite a* pour permuter ces colonnes entre elles et produire a**
La portée de l'invention ne se limite pas aux modes de réalisation décrits et représentés mais s'étend, bien au contraire, aux modifications et perfectionnements à la portée de l'homme du métier. According to a variant not shown, the triplet (a, b, c) is constructed as follows:

a (x) and b (x) = a (x) .h (x) 1g (x) are defined as above, - given a polynomial g2 (x) chosen such that the smallest integer N2 such that g2 (x) divides the polynomial xN2 -1 is equal to the smallest integer NO such that g (x) divides the polynomial xN0 - 1, we choose a permutation P which transforms any word of the binary cyclic code of length NO and generator polynomial g (x) in one word of the binary cyclic code of length N2 and of generator polynomial g2 (x). We note that such a permutation exists only for polynomials g2 (x) generating cyclic codes equivalent to Cg. This verification is well known to those skilled in the art and we refer for this to page 234 of the book of Mrs. FJ MAC WILLIAMS and MNJA SLOANE mentioned above; according to the invention, the permutation which, from the sequence a, associated with the polynomial a (x) divisible by g (x), produces the sequence a **, associated with the polynomial a ** (x), divisible by g2 (x) is then produced by any permutation producing from a (x) a first sequence a * (x) divisible by g (x) as explained above, followed by the permutation P which we have just introduced and which acts on the columns of the array with M rows and NO columns containing first a and then a * to swap these columns between them and produce a **
The scope of the invention is not limited to the embodiments described and shown but extends, on the contrary, to the modifications and improvements within the scope of the skilled person.

 In particular, the transition to yields of a quarter or less by adding one or more additional interleavers is done for each interleaver, by applying the principles stated above. In all these cases, the use of punching can be done to raise the output of the

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 code. It is recalled that punching consists in transmitting only a part of the control symbols.

 Moreover, the realization of the devices of the present invention is advantageously made by implementing, for performing the arithmetic calculations, polynomial multiplication, polynomial division, the interleaving function and the elementary decoding functions, dedicated circuits. does not include a processor (such a processor can, nevertheless, be used for controlling the operation of these devices). The use of such dedicated circuits makes it possible to achieve higher information rates.

 It is observed that, in the first embodiment, the output is, without punching, close to one-third, since for a sequence of n-m symbols to be encoded, there are two sequences of n control symbols.

II - SECOND MODE OF REALIZATION
In the second embodiment of the present invention, yields greater than 1/3, obtained without punching, are considered: for two sequences of nm symbols to be encoded, two sequences of n control symbols are provided, for example yield close to a half.

 Before beginning the description of the second embodiment, the mathematical foundations of its implementation are given below.

 To introduce the first embodiment, we presented a class of algebraic interleavers for use with turbochargers yielding close to one third. The main advantage of these interleavers is to preserve the divisibility of information polynomials by a given polynomial g (x) that partially characterizes the encoder. As a result, the error probability per bit of coded information is better independent of the position of the bits in the information sequence. As another advantage, the algebraic description of these interleavers makes their enumeration and evaluation

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 individual possible. In addition, it is hoped that the performance of this reduced interleaver game is representative of the performance of all interleavers.

 However, in many circumstances, for example in the context of wireless transmissions, better performance is required.

 The second embodiment is particularly interested in yields greater than or close to one half, without the use of punching methods.

 IIa - High efficiency turbocodes with "x to x" interleavers.

dans lequel h,,f, et g sont des polynômes à coefficients binaires d'indéterminée x représentant l'opérateur de délai. Consider the following systematic convolutional coder K x (K + 2):

where h ,, f, and g are polynomials with binary coefficients of indeterminate x representing the delay operator.

un K-uple a = (a1, ..., aK) de polynômes a, = EI=Oàn-1 a,,.x, avec des coefficients binaires a,; et l'information est codée en v = aG, qui est un (K+2)-uple de séquences d'indéterminée x :

Conventionally, the information transmitted is represented by

a K-uple a = (a1, ..., aK) of polynomials a, = EI = O-n-1 a ,, x, with binary coefficients a ,; and the information is encoded in v = aG, which is a (K + 2) -uple of sequences of indeterminate x:

It is observed that we write here sequences and not polynomials because the sums are not necessarily multiples of g and, if they are not, the division by g generates an infinite and finally periodic sequence.

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remplacer le dernier composant (E;-àK a,f,)lg de v par (L,=1àK a,f,)lg où as représente une séquence obtenue à partir de la séquences a, par permutation de ses coefficients. La transformation de chaque séquence a, en la séquence a1* s'appelle l'entrelacement (voir, par exemple l'article de MM. C. BERROU et A. GLAVIEUX intitulé "Near Optimum error-correcting coding and decoding : turbo-codes" publié par IEEE Transactions on Communication, Volume COM- 44, pages 1261 à 1271, en octobre 1996). To improve the performance of this type of encoder, you can

replace the last component (E; -à K a, f,) lg of v by (L, = 1 to K a, f,) lg where as represents a sequence obtained from the sequence a, by permutation of its coefficients. The transformation of each sequence in sequence a1 * is called interleaving (see, for example, the article by Messrs. C. BERROU and A. GLAVIEUX entitled "Near Optimum error-correcting coding and decoding: turbo-codes "published by IEEE Transactions on Communication, Volume COM-44, pages 1261 to 1271, October 1996).

 Figure 4 gives an illustration of an encoder performing this operation. In this figure, it can be observed that, for K input symbol sequences, the encoder outputs, - these identical K symbol sequences, - a control symbol sequence consisting of summing the products of the polynomials associated with information sequences a, by predetermined polynomials h, and dividing this sum by a predetermined polynomial g (encoder 401); a sequence of control symbols constituted by first interleaving each information sequence a, by an interleaver II (interleavers 402 to 405) to provide a sequence a, *, then performing the sum of the products of the polynomials associated with the sequences a, * by predetermined polynomials f, and dividing this sum by a predetermined polynomial g (encoder 406).

 It should be noted here that the set of interleavers II 402 to 406 illustrated in FIG. 4 is already a restriction of the interleaver 201 illustrated in FIG. 5, in which each sequence a can contain symbols of the sequence aJ with j different from i .

 According to general features of the present invention, in a representation where the binary data of each sequence a are classified in an array of NO columns and M lines, each interleaver /, comprises: at least one permutation in a set of permutations comprising , on the one hand, the automorphisms of the binary cyclic code of

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 NO length and generator polynomial g (x), permuting between them at least two of the NO columns of the array and, secondly, the permutations working only on data of the same column and exchanging between them at least two of said data and - no permutation outside said set.

 According to particular features of the present invention, there are applied to K / (K + 2) efficiency coders, with K representing an arbitrary positive integer value, "x to x" type interleaves described with respect to the first embodiment. which concerns the value K = 1.

We will describe, below, the case K> 2.

Let a polynomial g (x) = 1 + 91X + g2xz + ... + gm-1 xn-1 + x "'.

 Let NO be the smallest integer such that g (x) divides xN0 + 1.

 Finally, let n be an odd multiple of NO: n = M.NO.

The polynomial g (x) is then a divisor of the polynomial x "+ 1. For example, with g (x) = 1 + x + x4, n can be chosen from the values 15, 45, 75,
225, ..., 405, ... Further details regarding these divisibility properties can be found in the book by WW PETERSON and EJ WELDON entitled "Error-correcting codes" published by MIT Press, Cambridge, Mass., in 1972.

une terminaison, j=n-m à n-i (u,), xi , terminaison de m bits pour rendre le polynôme a, = u, + pnom à n-1 {Ui)j x1 divisible par g(x). The information is represented by a sequence u = (u1, uK) in which each of the K components u, is represented by a polynomial uj (x) of formal degree nm-1 with binary coefficients. At each polynomial u, (x), we add

a termination, j = nm to ni (u,), xi, ending of m bits to make the polynomial a, = u, + pnom to n-1 (Ui) j x1 divisible by g (x).

 The resulting K-uple a = (a1, aK) is then encoded to produce two control sequences.

par ,=1 a K a,'f/g, l'entrelacement de a,(x) en a,'(x) étant donné par : a/M = ajx6) modulo xn + 1 (2) The first is given by # @ = 1 to K a, h / g and it is a polynomial because the polynomial g (x) divides the K polynomials a,. The second is given

by, = 1 to K a, 'f / g, the interleaving of a, (x) into a,' (x) given by: a / M = ajx6) modulo xn + 1 (2)

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 where e is equal to a power of 2 (e = 2) taken modulo n. This type of permutation x to xe has been introduced in the first part concerning K = 1 and guarantees the divisibility of a, 'by g when a, is divisible by g.

 Let's now give some examples with K = 2.

spécifié par g(x) = 1 + x + x3 ; hi(x) = f2(x) = 1 + x2 + x3 ; h2(x) = W = 1 + x + X2 + x3 et n = 147. Consider a 2 x 4 turbocoder of the form described in (1) and

specified by g (x) = 1 + x + x3; hi (x) = f2 (x) = 1 + x2 + x3; h2 (x) = W = 1 + x + X2 + x3 and n = 147.

 With this value of n, 147, there are 42 numbers e which are each the residue, modulo 147, of a power of 2. For each of these values of e, the corresponding turbocode has been simulated on an additive white noise channel. Gaussian (known to those skilled in the art under the acronym "AWGN" for "Additive White Gaussian Noise"), for different values of ratio between the energy per Eb bit and the noise power per hertz (also called the density noise spectral), N.

The corresponding values of the curves of bit error rates ("BER") as a function of the signal-to-noise ratio, are represented in FIG. 6, for n = 147, K = 2 and for three different values of e: = 67 = 214, e = 32 = 25 and e
71 = 29. The first two values are representative of "good" values of e, among the 42 possible values, and the last value of e is representative of the few "less good" values: 1,2, 4,109, 142 and 50.

 With the same g (x), h, (x), f, (x), for i = 1 or 2, but with a higher value of n, the same simulations can be performed. The cases n = 413 and n = 917 have been selected because they offer a large number of values of different powers of 2, modulo n. For n = 413, there are actually 174 such different values, and for n = 917, there are 390 values such different values.

 The inventors have observed that no stage of the error curve appears to appear with the implementation of the present invention for a value of the error probability per bit after decoding of the order of 10-5, when the e value is judiciously chosen. We also note that the interlace of a, (x) to produce a, * (x) = a, (xe) modulo xn + 1 can be

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 for each value of i, with a value of e different but always of the form of a / -th power of 2: e = 2I. Preferentially, the same interleavers are used for all the values of i, which preserves the identity of the k-uples of symbols.

où g est un polynôme irréductible à coefficients binaires non divisible par un

polynôme carré. Cette matrice G code un triplet d'information u = (Yl, u2, u3) en : v = [a1, a2, a3, (ah)9 (akf)91 où a, est obtenu à partir de u, et a,' a partir de a,, comme exposé en regard du premier mode de réalisation. IIb- specification of turbochargers with K # 2
Consider, for example, the following 3 x 5 turbocharger:

where g is an irreducible polynomial with binary coefficients not divisible by a

square polynomial. This matrix G encodes a triplet of information u = (Y1, u2, u3) in: v = [a1, a2, a3, (ah) 9 (akf) 91 where a, is obtained from u, and a, from a, as discussed with respect to the first embodiment.

 One element that influences the minimum distance of such a code is the minimum number of non-zero components of 5-uple v.

 It is possible to guarantee that every 5-uple v = (v1, ..., v5) of the turbocode contains at least three non-zero sequences v ,.

To prove it, we explicitly write a, in a (xe) (reduced modulo x "+ 1), and we represent by" d "the inverse of e modulo n: ed = 1 (n), equation in which (n ) means modulo n.

Note that the equation a, () f, (x) = 0 modulo (x "+1) is equivalent to the equation a, (x) f, (xd) = 0 modulo (x" +1) .

 This results from the fact that e and d are relatively prime with n, so that for each b (x) of degree less than or equal to n-1, b (xe) and

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[a(x)f(x)]n(e) = [a(x)]"e [f(x)]n(e) modulo (x"+1 ). b (xd), taken modulo (xn + 1) are simply obtained by permutation of the coefficients of b (x), and that if we write [a (x)] n (e) the polynomial a (xe) modulo (xn) +1), ona:

[a (x) f (x)] n (e) = [a (x)] "e [f (x)] n (e) modulo (x" +1).

avec i différent de j, ne possède un déterminant qui est nul, modulo xN0 + 1. It follows from the theory of the so-called "MDS" codes (for "Maximum Separable Distance", in French separable at maximum distance "), that any non-zero v in the code generated by G will always contain at least three non-zero components, if the two following conditions are satisfied: - none of the polynomials h, and is no modulo xN0 + 1, where NO is the smallest integer such that g (x) divides xN0 + 1, NO being odd since the polynomial g ( x) is not divisible by any square of polynomial, and - no 2 x 2 matrix of the form

with i different from j, does not have a determinant that is null, modulo xN0 + 1.

A similar property is valid for any encoder of a turbocode of dimension K and of length N1, with a number of redundancies M1 = N1 - K> 2. In the latter case, the encoder looks like:

et toute séquence d'information u = (Y. 1 , .... uK) est d'abord codée en a = (Si 1, ..., aK), puis en :

and any sequence of information u = (Y. 1, .... uK) is first coded in a = (Si 1, ..., aK), then in:

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hl1lxd]), possède un déterminant non nul, modulo x+1. Let d be the inverse of e, modulo n: dJeJ = 1 (n). Each non-zero v in the code generated by G always contains at least N1-K + 1 non-null components if, for each integer r such that 1 <r <N1-K, each sub-matrix rxr of G is extracted from its N1 -K last columns and where h ,,, (x) is replaced by

hl1lxd]), has a nonzero determinant, modulo x + 1.

 It should be noted here that the decoding of turbocode redundancy N1 - K> 2 has already been considered. For example, see D. DIVSALAR and F. POLLARA, Multiple Turbocodes for Deep Space Communications, TDA Progress Report 42-121, May 15, 1995.

 Let us now describe a method for selecting good candidates to obtain a good K-type turbocode and length N1 with "x to x" interleavers.

 Consider first the case where N1-K = 2.

 Let us choose an irreducible polynomial g (x) on GF (2), degree m> 2 such that NO = 2m-1> N1 and take GF (2m) as the set of polynomial residues modulo g (x). Let n also be the odd multiple of NO.

ou a,, i = 1, N1, sont différents éléments non nuls de GF(2m) et r et s des entiers qui sont différents modulo NO. Le choix s = r +1 est, par exemple, toujours un bon choix. Ceci implique que toute sous matrice de # est non singulière. Soit #(1,2) la sous-matrice des deux premières colonnes de #, écrivons [#(1,2)]-1 1-de la manière suivante :

Let's construct a matrix Fà 2 rows and N1 columns:

or a ,, i = 1, N1, are different non-zero elements of GF (2m) and r and s are integers that are different modulo NO. The choice s = r +1 is, for example, always a good choice. This implies that any sub-matrix of # is non-singular. Let # (1,2) be the sub-matrix of the first two columns of #, write [# (1,2)] - 1 1-as follows:

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 or A is a 2 x K matrix on GF (2m). For a chosen value of e power of 2 modulo n, let us replace every element of the second line of A by its e-th power and note by # the transposed matrix of this matrix.

Let's then interpret the elements of # as polynomials of degree m-1 of indeterminate x, divide them by g (x) or by any other divisor polynomial of xN0 + 1 and call P (x) the resulting matrix.

Finally, let us define the matrix G of dimension K x (K + 2):
G = [IK P (x)] where IK is the identity matrix of dimension K.

 For each value of e, this encoder G can be used as a turbo encoder. By simulation, it is then possible to choose the best value of e.

The case N1 - K> 2 can be treated in a similar way. In this case, with M1 = N1 - K, we build a matrix of type M1 x N1:

Avec 111 ,M1) la sous-matrice des MI premières colonnes de F, on écrit (11,M1)]-' T'en [1M1 ] ou IM1 est la matrice identité de dimension M1 et A une sous-matrice sur GF(2m) de dimension M1 x K. Pour des valeurs choisies et = 2It, pour t = 2, ..., M1, on remplace les éléments de la t-ième ligne de # par leur puissance et - ième.

With 111, M1) the sub-matrix of the first MI columns of F, we write (11, M1)] - 'T'en [1M1] where IM1 is the identity matrix of dimension M1 and A a sub-matrix on GF ( 2m) of dimension M1 x K. For selected values and = 2It, for t = 2, ..., M1, we replace the elements of the th-th line of # by their power and - th.

 We then write # by the transposed matrix of this matrix, we interpret the elements of # as polynomials of degree m-1 of indeterminate x, we divide them by g (x) and we call P (x) the resulting matrix of dimensions K x (N - K).

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 The G = [IK P (x)] coders obtained for different values of the (M1-1) -uple (e2, eM1) are then analyzed by simulations and the best ones can be selected.

 IIc - Description of an implementation of the second embodiment of the present invention.

 The description of the second embodiment of the present invention will now be continued with reference to FIGS. 7 and 8, for K = M1 = 2.

 FIG. 7 schematically illustrates the constitution of a network station or computer coding station, in the form of a block diagram. This station comprises a keyboard 711, a screen 709, an external information source 710, a radio transmitter 706, jointly connected to an input / output port 703 of a processing card 701.

 The processing card 701 comprises, interconnected by an address and data bus 702: a central processing unit 700; a random access memory RAM 704; a ROM memory 705; and - the input / output port 703.

 Each of the elements illustrated in Figure 7 is well known to those skilled in the field of microcomputers and transmission systems and, more generally, information processing systems. These common elements are therefore not described here. It is observed, however, that: the information source 710 is, for example, an interface device, a sensor, a demodulator, an external memory or another information processing system (not shown), and is preferentially adapted to provide signal sequences representative of speech, service messages or multimedia data, in the form of binary data sequences,

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 the radio transmitter 706 is adapted to implement a packet transmission protocol over a non-wired channel and to transmit these packets on such a channel.

 It is further observed that the word "register" used in the description designates, in each of the memories 704 and 705, both a memory area of low capacity (a few binary data) and a memory area of large capacity (allowing store an entire program).

- un registre "données~primaires" dans lequel sont conservées, dans l'ordre de leur arrivée sur le bus 702, les données binaires en provenance de la source d'information 710, sous forme de deux séquences, u1 et u2, complétées ensuite pour former deux séquences a1 et a2, - un registre "nb~données" qui conserve un nombre entier correspondant au nombre de données binaires n-m dans le registre "données~binaires",

- un registre "données-permutées" dans lequel sont conservées, dans l'ordre de leur transmission sur le bus 702, les données binaires permutées, comme décrit en regard de la figure 8, sous forme de deux

séquences,a?* et a2*, - un registre "reste~intermédiaire" dans lequel sont conservés successivement les restes intermédiaires des divisions, registre utilisé pour construire chaque séquence a, à partir de la séquence u, correspondante,

- un registre "reste finaP' dans lequel sont conservées des données binaires complémentaires, sous forme de deux séquences, et - des registres "a,, bi, çl" et "a2, b2, Ç2" dans lesquels sont conservées, dans l'ordre de leur détermination par l'unité centrale 700, les données binaires des séquences. The RAM 704 stores data, variables and intermediate processing results, in memory registers carrying, in the description, the same names as the data whose values they retain. RAM 704 comprises in particular:

a register "data ~ primary" in which are preserved, in the order of their arrival on the bus 702, the binary data from the source of information 710, in the form of two sequences, u1 and u2, completed then to form two sequences a1 and a2, - a register "nb ~ data" which keeps an integer corresponding to the number of binary data nm in the register "data ~ binary",

a "data-permutated" register in which, in the order of their transmission on the bus 702, the permuted bit data are stored, as described with reference to FIG. 8, in the form of two

sequences, a? * and a2 *, - a register "remainder ~ intermediate" in which are conserved successively the intermediate remains of the divisions, register used to construct each sequence a, from the sequence u, corresponding,

a "remainder" register in which complementary binary data are stored in the form of two sequences, and "a ,, b1, b1," and "a2, b2, C2" registers in which are stored in order of their determination by the CPU 700, the binary data of the sequences.

<Desc / Clms Page number 43>

- la séquence h = hl = f2, dans le registre "h", - la séquence f fi = h2, dans le registre "T', - la valeur de NO, dans un registre "NO", - la valeur de N1, dans un registre "N1", - la valeur de M1, dans un registre "M1", - la valeur de M, dans un registre "M", - le tableau définissant l'entrelaceur agissant sur la séquence a1, dans un registre "entrelaceur1", et - le tableau définissant l'entrelaceur agissant sur la séquence a2, dans un registre "entrelaceur2". The read-only memory 705 is adapted to keep, in registers which, for convenience, have the same names as the data they retain: the operating program of the central processing unit 700, in a "program" register, the sequence g, in a register "g", the degree m of g (x), in a register "degree"

the sequence h = h1 = f2, in the register "h", the sequence ff = h2, in the register "T", the value of NO, in a register "NO", the value of N1, in a register "N1", - the value of M1, in a register "M1", - the value of M, in a register "M", - the array defining the interleaver acting on the sequence a1, in a register " interleaver1 ", and - the array defining the interleaver acting on the sequence a2, in a register" interleaver2 ".

 The interleavers considered here are respectively of type "x to xe1" and "x to xe2" described above.

 The central processing unit 700 is adapted to implement the flowchart described in FIG. 8.

 In FIG. 8, which represents the operation of an encoder as illustrated in FIG. 7, it is observed that, after an initialization operation 800, during which the registers of the random access memory 704 are initialized (nb ~ data = "0"), during an operation 801, the central unit 700 waits to receive, then receives a binary data to be transmitted, positions it in random access memory 704, in the "primary data" register and increments the counter " nb data ".

 It can be observed here that, to constitute the two sequences Y.1 and u2, the central unit 700 first constitutes the sequence u1 and then the sequence u2 with the primary data from the information source 710.

<Desc / Clms Page number 44>

 Then, during a test 802, the CPU 700 determines whether the whole number stored in the register "nb ~ data" is equal to the product M.NO to which is subtracted the degree m of g (x ), M, NO and the degree m of g (x) being values stored in read-only memory 705.

"données-primaires", par le polynôme g(x) sont effectuées, jusqu'aux derniers termes (de plus haut degrés) de u(x) et U2(X), en mettant en #uvre, à cet effet, le registre "resfe intermédiaire". Les restes de ces divisions sont mis en mémoire dans le registre "reste naP'. Les résultats de ces divisions fournissent les premiers éléments des séquences 121 = a1/g et b2 = a2/g. When the result of the test 802 is negative, the operation 801 is repeated. When the result of the test 802 is positive, during an operation 803, the divisions of the polynomials u1 (x) and u2 (x) respectively associated with the binary data sequences u1 and u2 stored in the register

"primary data", by the polynomial g (x) are carried out, up to the last terms (of higher degrees) of u (x) and U2 (X), by implementing, for this purpose, the register "intermediate resf." The remains of these divisions are stored in the register "remain naP." The results of these divisions provide the first elements of the sequences 121 = a1 / g and b2 = a2 / g.

conservées dans le registre "reste frnaP' sont respectivement juxtaposées aux fins des séquences u1 et u2 pour former les séquences a1 et a2. Les données binaires des séquences a1 et a2 sont mises en mémoire dans les registres "a1,

1211 pi" et "a2, b2, C2". Then, during an operation 804, the binary data

stored in the register "remain frnaP" are respectively juxtaposed for the purposes of the sequences u1 and u2 to form the sequences a1 and a2 The binary data of the sequences a1 and a2 are stored in the registers "a1,

1211 pi "and" a2, b2, C2 ".

dans les registre "ai, b1t ç" et "a2, b2, ç2". Then, during an operation 805, the divisions performed during the operation 803 are continued, with the additional data added during the operation 804 and the sequences b1 and b2 are completed.

in the register "ai, b1t ç" and "a2, b2, ç2".

successivement lues dans le registre "ah Pl, pi", dans l'ordre décrit par le tableau "entrelaceur1" conservé en mémoire morte 705, et - les données binaires de la séquence a2 sont respectivement et successivement lues dans le registre "a2, b2, c2", dans l'ordre décrit par le tableau "entrelaceur2" conservé en mémoire morte 705. Then, during an operation 806: the binary data of the sequence a1 are respectively and

successively read in the register "ah Pl, pi", in the order described by the table "interleaver1" stored in read-only memory 705, and - the binary data of sequence a2 are respectively successively read in the register "a2, b2 , c2 ", in the order described by the" interleaver2 "table stored in read-only memory 705.

 The data that successively results from these readings are respectively stored in the "data ~ permuted" register of the RAM 704.

<Desc / Clms Page number 45>

"données~permutées", par le polynôme g(x) sont effectuées, en mettant en #uvre, à cet effet, le registre "/'ese~//ef77?éd/a/re". Les résultats de ces divisions sont mis en mémoire dans le registre "a, th ç" et "a2, b2, Ç2", et correspondent aux données binaires des séquences c1 et c2. Then, during an operation 807, the polynomial divisions a1 * (x) and a2 * (x) respectively associated with the permuted binary data sequences stored in the register

"data ~ permuted" by the polynomial g (x) are performed, implementing, for this purpose, the register "/ 'ese ~ // ef77? ed / a / re". The results of these divisions are stored in the register "a, th ç" and "a2, b2, Ç2", and correspond to the binary data of the sequences c1 and c2.

121, pl" et "a2, b2, P2" de la mémoire vive 704, respectivement par les polynômes h(x) et f(x) ; - la séquence cs est déterminée en effectuant le produit des polynômes associés aux séquences c1 et c2 conservées dans les registres "a1,

b, pl" et "a2, b2, P2" de la mémoire vive 704, respectivement par les polynômes f(x) et h(x). During an operation 808 two so-called "control" or "redundant" sequences are determined: the sequence bs is determined by producing the product of the polynomials associated with the sequences 121 and b2 stored in the "a1" registers,

121, pl "and" a2, b2, P2 "of the random access memory 704, respectively by the polynomials h (x) and f (x) - the sequence cs is determined by producing the product of the polynomials associated with the sequences c1 and c2 kept in the registers "a1,

b, pl "and" a2, b2, P2 "of the random access memory 704, respectively by the polynomials f (x) and h (x).

It is observed that, thanks to the invention, memory elements are obtained by dividing by g (x) before multiplications by h (x) or f (x).

Nb données est remis à "0" et l'opération 801 est réitérée. During an operation 809, the sequences ai, a2, bs and fus are emitted using, for this purpose, the transmitter 706. Then, the registers of the memory 704 are, again, initialized, in particular the counter

Nb data is reset to "0" and operation 801 is repeated.

 It is observed here that, alternatively, during the operation 809, the sequences a1 and a2 are transmitted integrally, but only a subset, for example every other data, of each of the sequences bs and cs is emitted. This variant is known to those skilled in the art under the name of punching.

 As regards the decoding, it is observed that by knowing the polynomials g (x), h (x), f (x) and the interleavers G1 and G2 which, from the sequences a1 and a2 respectively provide the permuted sequences a1 * and

<Desc / Clms Page number 46>

séquences (fi1, a2, bs, p,) en utilisant les entrelaceurs considérés ci-dessus et, éventuellement les désentrelaceurs correspondants. a2 *, the person skilled in the art knows, without any technical problem, making the decoder suitable for decoding and error correction affecting the quadruplet of

sequences (fi1, a2, bs, p,) using the interleavers considered above and, optionally, the corresponding de-interlacers.

 FIG. 9 shows that a decoding device adapted to decode the sequences transmitted by the decoding device illustrated in FIGS. 4 to 8, essentially comprises: a decoder 901 corresponding to the encoder 401, which receives the estimates of the transmitted sequences , v1 to vK + 1 as well as K extrinsic information sequence w "'1 to w" K discussed below, and provides K posterior estimation sequences w1 to Wk, K interleavers 902, identical to interleavers 402 to 405 used in the encoder, which respectively receive the sequences w1 to wK and interleaves respectively w'1 to w'K.

séquences W"1 à w'K et fournissant les séquences W"'1 à w"K. a second decoder 903, corresponding to the encoder 406 and receiving the sequences w'1 to w'K and the sequence YK + 2, and on the one hand furnishes K posterior estimation sequences w "1 to w" K and on the other hand, an estimated sequence of 'and K K deinterlacers 904, inverse of the interleaver 402 to 405, receiving the

sequences W "1 to w'K and providing the sequences W"'1 to w "K.

 The estimated sequence is taken into account only after a predetermined number of iterations (see the article "Near Shannon Limit errorcorrecting coding and decoding: turbocodes" cited above).

 According to the present invention, the interleavers and de-interleavers used in the decoding each have the same characteristics as the interleavers used in the coding and, preferably, are of the "x to x" type. Preferably, the coding as well as the decoding, with a value of identical, the exponents eIJ are equal. Preferably also, at coding as at decoding, the values of exponents e ,, are all powers of 2.

<Desc / Clms Page number 47>

 In addition, the decoders 901 and 903 are initialized taking into account the fact that the encoders 401 and 406 each have an initial state and a zero final state.

 Regarding decoding, the reader may refer to: - the article by MM. L.R. BAHL, J. COCKE, F. JELINEK and J.

RAVIV entitled "Optimal decoding of linear codes for minimizing symbol error rate", published in IEEE Transactions on Information Theory, March 1974; - in the article of MM. J. HAGENAUER, E. OFFER and L. PAPKE entitled "Iterative decoding of binary block and convolutional codes" published in the journal IEEE Transactions on Information Theory, March 1996; - in the article of MM. J. HAGENAUER and P. HOEHER entitled "A viterbi algorithm with soft decision outputs and its applications", published with the proceedings of the IEEE GLOBECOM conference, pages 1680-1686, in November 1989; - in the article of MM. J. HAGENAUER, P. ROBERTSON and L.

PAPKE entitled "Iterative (turbo) decoding of systematic convolutional codes with MAP and SOVA algorithms", published by the magazine Informationstechnische Gesellschaft (ITG) Fachbericht, pages 21-29, October 1994; - in the article of MM. C. BERROU, S. EVANO and G. BATTAIL, entitled "Turbo-block-codes" and published with the minutes of the "turbo coding" seminar organized by the Lünd Institute of Technology (Sweden) (Department of Electronics applied in August 1996.

Claims (27)

1. Coding method characterized in that: 1 / it takes into account: a predetermined integer M1, equal to or greater than 2, a number K, greater than or equal to 2, of sequences a, (i = 1, ..., K) of binary data representative of a physical quantity, each sequence a, having: # a polynomial representation a, (x) multiple of a predetermined polynomial g, (x), and # a number of binary data equal to the product of any integer M by the integer NO, smaller integer such that the polynomial xN0 + 1 is divisible by each of the polynomials g, (x); 2 / it comprises a first operation of producing a number K * M1 of

 sequences said permuted, a ,, *, (i = 1, ..., K; j = 1, ..., M1) (806), each sequence aIJ * - being obtained by a permutation of the sequence a; corresponding, said permutation being, in a representation where the binary data of each sequence a, are written, row by row, in an array with NO columns and M rows, the resultant of any number of so-called elementary permutations which each: # has the property of transforming the cyclic code of length NO and generator polynomial g, (x) into an equivalent cyclic code of generating polynomial gIJ (x) which can be equal to g, (x), and acts by permutation on the NO columns of the table representing a ,, # is any permutation of the symbols of a column of that table; and - having, accordingly, a polynomial representation a ,, * (x) which is equal to a polynomial product c ,, (x) g ,, (x), <Desc / Clms Page number 49>  c ,, (x), for j = 1, ..., M9, each polynomial flx) being a polynomial of degree at most equal to the degree of the polynomial g ,, (x) of the same indices i and j.

 at least one permuted sequence aIJ * being different from the corresponding sequence a 3 / it comprises a second operation of production of M1 redundant sequences (807 to 809) whose polynomial representation is equal to E fIJ (x)  2. Coding method characterized in that: 1 / it takes into account: a predetermined integer M1, equal to or greater than 2,

 a number K, greater than or equal to 2, of sequences a, (i = 1, ..., K) of binary data representative of a physical quantity, each sequence a, having: # a polynomial representation a, (x ) multiple of a predetermined polynomial g, (x) and without multiple polynomial factors, and # a number of binary data equal to the product of an odd integer M by the integer NO, smaller integer such that the polynomial xN0 +1 is divisible by each of the polynomials g, (x); 2 / it comprises a first operation of producing a number K * M1 of

 sequences said permuted, a ,, *, (i = 1, ..., K; j = 1, ..., M9) (806), each sequence a ,, * having a polynomial representation equal to a ,, * (x) = a, * (x4) modulo (xn + 1), where - n is the product of the number M by the integer NO, e ,, is a relatively prime number with n - cI} is the quotient of a ,, * (x) by g ,, (x), - the polynomial g ,, (x) is the generator polynomial of the smallest cyclic code of length NO containing the polynomial gI (xeIJ) modulo (xN0 + 1), at at least one permuted sequence aIJ * being different from the corresponding sequence a; <Desc / Clms Page number 50>  c ,, (x), for / = 1, ..., M7, each polynomial f ,, (x) being a predetermined polynomial of degree at most equal to the degree of the polynomial g ,, (x) of the same indices / and j.

 3 / it comprises a second operation for producing M1 redundant sequences (807 to 809) whose polynomial representation is equal to E fIJ (x)  3. Coding method according to claim 2, characterized in that, during the first production operation, all the values of the exponents e ,, having the same value of the index j are identical.  4. Encoding method according to any one of claims 2 or 3, characterized in that, during the first production operation, all the values of exponents eIJ are equal to a power of 2.  5. Coding method according to any one of claims 1 to 4, characterized in that it comprises a transmission operation on the one hand the sequences a ,, and, on the other hand, a subset of data from other sequences.  6. Encoding device characterized in that it comprises a processing means adapted to: 1 / take into account: a predetermined integer M1, equal to or greater than 2,

 a number K, greater than or equal to 2, of sequences a, (i = 1, ..., K) of binary data representative of a physical quantity, each sequence a, having: # a polynomial representation a, (x ) multiple of a predetermined polynomial g, (x), and # a number of binary data equal to the product of any integer M by the integer NO, smaller integer such that the polynomial xN0 + 1 is divisible by each polynomials g, (x); <Desc / Clms Page number 51>  equal to E f ,, (x) c ,, (x), for j = 1, ..., M1, each polynomial f ,, (x) being a polynomial of degree at most equal to the degree of the polynomial g ,, (x) same indices i and j.

 a ,, * (x) which is equal to a polynomial product c ,, (x) g, (x), - at least one permuted sequence aIJ * being different from the corresponding sequence a, 3 / producing M1 redundant sequences of which the polynomial representation is

 (i = 1, ..., K; j = 1, ..., M9), each sequence ali - being obtained by a permutation of the sequence a, corresponding, said permutation being, in a representation where the binary data of each sequence a, are written, line by line, in an array with NO columns and M rows, the resultant of any number of so-called elementary permutations, each of which: # has the property of transforming the cyclic code of length NO and of generator polynomial g, (x) into an equivalent cyclic code of generator polynomial gIJ (x) which may be equal to g, (x), and acts by permutation on the NO columns of the array representing aj, # is any permutation of symbols of a column of said table; and - having, accordingly, a polynomial representation

 2 / production of a number K * M1 of sequences called permuted, aIJ *,  7. Encoding device characterized in that it comprises a processing means adapted to: 1 / take into account: a predetermined integer M1, equal to or greater than 2,

 a number K, greater than or equal to 2, of sequences a, (i = 1, ..., K) of binary data representative of a physical quantity, each sequence a, having: <Desc / Clms Page number 52>  equal to E f ,, (x) c ,, (x), fory = 1, ..., Mf, each polynomial f ,, (x) being a predetermined polynomial of degree at most equal to the degree of the polynomial g ,, (x) same indices i and j.

 2 / produce a number K * M9 of sequences called permuted, a ,, *, (i = 1, ..., K; j = 1, ..., M9), each sequence a ,, * having a polynomial representation equal to a,} * (x) = a, * (J1) modulo (x "+1), where - n is the product of the number M by the integer NO, - eIJ is a relatively prime number with n - c ,,, is the quotient of a ,, * (x) by g ,, (x), - the polynomial g ,, (x) is the generator polynomial of the smallest cyclic code of length NO containing the polynomial gI (xeij) modulo (xN0 + 1), at least one permuted sequence aij * being different from the corresponding sequence a; 3 / producing M1 redundant sequences whose polynomial representation is

 # a polynomial representation a, (x) multiple of a predetermined polynomial g, (x) and without multiple polynomial factors, and # a number of binary data equal to the product of an odd integer M by the integer NO, smaller integer such that the polynomial xN0 + 1 is divisible by each of the polynomials g, (x);  8. Encoding device according to claim 7, characterized in that the processing means is adapted to implement exponents e ,, which, when they have the same value of the index j, are identical.  9. Encoding device according to any one of claims 7 or 8, characterized in that the processing means is adapted to implement exponents e ,, which each have a value equal to a power of 2. <Desc / Clms Page number 53>  10. Encoding device according to any one of claims 6 to 9, characterized in that it comprises a transmission means adapted to transmit, on the one hand, the sequences a ,, and on the other hand, a sub all the data of the other sequences.  11. Decoding method characterized in that 1 / it takes into account: - a predetermined integer M1, equal to or greater than 2, - a number K, greater than or equal to 2, of sequences a, (/ = 1,. .., K) of data representative of a physical quantity, each sequence a, having: # a polynomial representation a, (x) multiple of a predetermined polynomial g, (x), and # a number of binary data equal to produces any integer M by the integer NO, smaller integer such that the polynomial xN0 + 1 is divisible by each of the polynomials g, (x); 2 / it comprises a parallel turbodecoding operation of K symbol sequences implementing the divisor polynomials g ,, (x). 3 / it comprises, for each a ,, M1 operations of permutation, of which at least one is not the identity, each permutation being, in a representation where the binary data of each sequence a, are written line by line, in a table with NO columns and M rows, the resultant of any number of so-called elementary permutations, each of which: # has the property of transforming the cyclic code of length NO and of generator polynomial g, (x) into a code cyclic equivalent of generator polynomial g ,, (x) being able to be equal to g, (x), and acts by permutation on the NO columns of the array representing a ,, # is any permutation of the symbols of a column of said array. <Desc / Clms Page number 54>  12. Decoding method characterized in that 1 / it takes into account: - a predetermined integer M1, equal to or greater than 2, - a number K, greater than or equal to 2, of sequences a, (i = 1 ,. .., K) of data representative of a physical quantity, each sequence a, having: # a polynomial representation a, (x) multiple of a predetermined polynomial g, (x) and without multiple polynomial factors, and # a number of binary data equal to the product of an odd integer M by the integer NO, smaller integer such that the polynomial xN0 + 1 is divisible by each of the polynomials g, (x); 2 / it comprises a parallel turbodecoding operation of K symbol sequences implementing the divide polynomials g ,, (x), 3 / said parallel turbodecoding operation comprising a

 permutation producing so-called permuted sequences, a ,, *, (i = 1, ..., K; j = 1, ..., M1), each permuted sequence a, J * having a polynomial representation equal to a ,, * (x) = a, * (xe4) modulo (x "+1), where: - n is the product of the number M by the integer NO, - eIJ is a relatively prime number with n - c ,, is the quotient of aIJ * (x) by g ,, (x), - the polynomial gIJ (x) is the generating polynomial of the smallest cyclic code of length NO containing the polynomial gI (xIJ) modulo (xN0 + 1), at least a permuted sequence a ,, * being different from the corresponding sequence a.  13. Decoding method according to claim 12, characterized in that, during the permutation operation, all the values of the exponents eIJ having the same value of the index j are identical. <Desc / Clms Page number 55>  14. Decoding method according to any one of claims 12 or 13, characterized in that, during the permutation operation, all the values of the exponents e ,, are equal to a power of 2.  15. Decoding method according to any one of claims 11 to 14, characterized in that it comprises a receiving operation on the one hand of sequences a ,, and, on the other hand, a subset of data of other sequences resulting from coding of the sequences aI.  16. A decoding device characterized in that it comprises a suitable processing means: 1 / to take into account: a predetermined integer M1 equal to or greater than 2; a number K, greater than or equal to 2; a, (i = 1, ..., K) of data representative of a physical quantity, each sequence a, having: # a polynomial representation a, (x) multiple of a predetermined polynomial g, (x), and # a number of binary data equal to the product of any integer M by the integer NO, smaller integer such that the polynomial xN0 + 1 is divisible by each of the polynomials g, (x); 2 / to perform a parallel turbodecoding operation of K symbol sequences implementing the divide polynomials g ,, (x). 3 / to perform, for each a ,, M1 permutation operations, at least one of which is not the identity, each permutation being, in a representation where the binary data of each sequence a, are written, line by line, in a table with NO columns and M rows, the resultant of any number of so-called elementary permutations, each of which: # has the property of transforming the cyclic code of length NO and of generator polynomial g, (x) into a code <Desc / Clms Page number 56>  cyclic equivalent of generator polynomial gij (x) may be equal to g, (x), and acts by permutation on the NO columns of the array representing a ,, # is any permutation of the symbols of a column of said array.  17. A decoding device characterized in that it comprises a suitable processing means: 1 / to take into account: a predetermined integer M1, equal to or greater than 2,

 a number K, greater than or equal to 2, of sequences a, (i = 1, ..., K) of data representative of a physical quantity, each sequence a, having: # a polynomial representation a, (x) multiple of a predetermined polynomial g, (x) and without multiple polynomial factors, and # a number of binary data equal to the product of an odd integer M by the integer NO, smaller integer such that the polynomial xN0 + 1 is divisible by each of the polynomials g, (x); 2 / to carry out a parallel turbodecoding operation of K symbol sequences implementing the divide polynomials gIJ (x), 3 / to perform a permutation operation producing said sequences

   permuted, a ,, *, (i = 1, ..., K; j = 1, ..., M1), each permuted sequence a ,, * having a polynomial representation equal to a ,, * (x) = a, * (X '') modulo (X '+ 1), where: - n is the product of the number M by the integer NO, eIJ is a relatively prime number with n

 - c ,, is the quotient of a ,, * (x) by g, f (x), - the polynomial g ,, (x) is the generating polynomial of the smallest cyclic code of length NO containing the polynomial gI (xeIJ ) modulo (xN0 + 1), <Desc / Clms Page number 57>  at least one permuted sequence aIJ * being different from the corresponding sequence a.  18. A decoding device according to claim 17, characterized in that the processing means is adapted to implement values of the exponents eIJ which are identical, when said exponents have the same value of the index j.  19. Decoding device according to any one of claims 17 or 18, characterized in that the processing means is adapted to implement values of exponents and) which are each equal to a power of 2.  20. Decoding device according to any one of claims 11 to 14, characterized in that it comprises a receiving means adapted to receive, on the one hand sequences a ,, and, secondly, a subset of the data of other sequences resulting from coding of the sequences a ,.  21. Apparatus for processing representative speech signals, characterized in that it comprises a coding device according to any one of claims 6 to 10 or a decoding device according to any one of claims 16 to 20.  22. A data transmission device comprising a transmitter adapted to implement a packet transmission protocol, characterized in that it comprises a coding device according to any one of claims 6 to 10 or a decoding device according to the invention. any one of claims 16 to 20 or a speech representative signal processing device according to claim 21. <Desc / Clms Page number 58>  23. Data transmission device according to claim 22, characterized in that said protocol is the ATM protocol (acronym for the words "Asynchronous Transfer Mode") asynchronous transfer mode.  24. Data transmission device according to claim 22, characterized in that said protocol is an ETHERNET type protocol.  25. A data transmission device comprising an emitter emitting on a non-wire channel, characterized in that it comprises a coding device according to any one of claims 6 to 10 or a decoding device according to any one of the claims. 16 to 20.  26. Apparatus for processing sequences of signals representative of at most one thousand binary data, characterized in that it comprises a coding device according to any one of claims 6 to 10 or a decoding device according to any one of claims 16 to 20.  27. Network station, characterized in that it comprises a coding device according to any one of claims 6 to 10 or a decoding device according to any one of claims 16 to 20.