FR2800950A1 - Interleaving method e.g. for turbocoding of data, involves considering a matrix having r rows and m columns, filled row by row by the successive numbers from 0 to r tom-1 - Google Patents

Abstract

The method involves considering a matrix S having r rows and m columns, filled row by row by the successive numbers from 0 to r to m-1, Each column in the matrix S is divided into a predetermined number lambda of sub- columns, such that r/ lambda is not prime. The sub-columns of S equal in number to lambda .m are designated by S lambda 1 less than lambda 2 greater with 0 less than or equal to lambda 1 less than or equal to lambda -1 and 0 less than or equal to lambda 2 less than or equal to m-1 where lambda 2 refers to the column of S where S lambda 1 less than lambda 2 greater than appears and lambda 1 refers to the position of the sub-column S lambda 1 less than lambda 2 greater than in the column of index lambda 2. Each sub-column S lambda 1 less than lambda 2 greater than is then written in the form of a matrix with R rows and M columns (with r/ lambda = RM) and in this form it is interleaved by an interleaver of the so-called wheel type defined by a circular permutation of each column of said matrix with R rows and M columns, the interleaver not being identity. This matrix with R rows and M columns is reconverted, after the circular permutations on its columns, into a sub-column S asterisk lambda 1 which will occupy, in a matrix S asterisk , the same position as that occupied by S lambda 1 in the matrix S. The permutation table consists of pairs each formed by an element of the matrix S and the element with the same position in the matrix S asterisk . An Independent claim is included for a coding method, a decoding method, a turbodecoding method, coding device, a turbo decoding device, a turbodecoding device, a device for processing signals, a data transmission device, and a network station.

Description

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The invention is in the general field of information transfer methods. It relates more particularly to a method and a data interleaving device forming part of a transmission or reception method.

The invention finds its place in the general field of data coding with a view to their transmission and reception, for example by a radio system. Coders of a particular type known as “turbocoders” (as well as the associated decoding devices known as “turbodecoders”) described for example in previous patents by the same applicant are known in a conventional manner in this field. Such a turbocoder and the associated decoder use one or more data interleaving devices.

The present invention relates to an interlacing and deinterlacing method, intended to form part of such a so-called "turbocoding" method and of the associated turbodecoding method.

The present invention applies equally well to the coding (in English "encoding") of data representative of a physical quantity, to the coding of data capable of modulating a physical quantity, to the decoding of signals modulated in the form of data, as well as to decoding of data representative of physical quantities or the management of data transmissions. These data can, for example, represent images, sounds, computer data, electrical quantities, or stored data.

When convolutional encoders are used to implement iterative decoding using elementary decoders with soft inputs and outputs, these codes are greatly improved when their encoders contain a permutation device called an interleaver, a device for permutation allowing to return to the initial sequence being then called "deinterleaver". In this case, they are usually called turbocoders (in English “turbo-encoder”) and the corresponding iterative decoder is called a turbodecoder. For convenience :

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- the operation performed by the turbo-encoder is called a turbo-coding and this operation provides a so-called turbo-coded sequence the operation performed by the turbo-decoder is called a turbo-decoding and this operation provides a so-called sequence turbo-decoded.

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

The aim of the present invention is to provide more efficient interleavers for a turbocoder, i.e. allowing a greater minimum distance to be obtained. This is especially important when the signal-to-noise ratio of the channel is relatively high, because this is can then reduce the decoding error rate and therefore avoid having to resend incorrectly received data.

It is briefly recalled here that a turbocode exhibits different behavior depending on the value of the signal-to-noise ratio of the channel. If the signal-to-noise ratio is large, the minimum weight of the non-zero words in the turbocode and the number of such minimum weight words predominate in determining the performance of the turbocode. On the contrary, if the signal to noise ratio is low, it seems that it is the number of code words of weight close to a value greater than or equal to the minimum weight of the code that influences the performance of the turbodecoder.

The invention relates firstly to a method of creating a permutation table, characterized in that said table matches each input rank from 0 to rm-1 to an output rank from 0 to rm-1, said process comprising the following steps:
E1- we consider a matrix S comprising r rows and m columns,

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avec 0 S /1 <l-1 et 0 </2 <m-1 où h fait référence à la colonne de S où apparaît Sl1l2 et où ll fait référence à la position de la sous-colonne Sl1l2 dans la colonne d'indice l2. filled line by line by successive numbers from 0 to rm-1
E2- each column of said matrix S is split into a predetermined number l of sub-columns, such that r / l is not prime,
E3- the sub-columns of S in number equal to lm are designated by SI, 12

with 0 S / 1 <l-1 and 0 </ 2 <m-1 where h refers to the column of S where appears Sl1l2 and where ll refers to the position of sub-column Sl1l2 in the index column l2.

E4- each sub-column SI, 12 is then written in the form of a matrix with N rows and M columns (with r / l = NM) and in this form it is interlaced by a so-called "lock" type interleaver defined by a circular permutation of each column of said matrix with N rows and M columns, said interleaver not being the identity,
E5- this matrix with N rows and M columns is reconverted, after said circular permutations on its columns, into a sub-column S * l1l2 which will occupy in a matrix S * the same place as that occupied by SI, 12 in the matrix S,
E6- the permutation table consists of couples each formed of an element of the matrix S and of the element of the same position of the matrix S *.

colonne /2 (0 sl2 sm-1) de la matrice S* une modification de l'ordre d'apparition des sous-colonnes S*l1l2 dans ladite colonne. Preferably, the method also comprises in at least one

column / 2 (0 sl2 sm-1) of the matrix S * a modification of the order of appearance of the sub-columns S * l1l2 in said column.

According to a preferred implementation, the same latch interleaver is used to produce each of the sub-columns S * l1l2 of a given column l2 of the matrix S *.

According to a particular implementation, the sub-columns of at least two columns of the matrix S * are produced by different latch interleavers.

According to a more particular implementation, the m lock interleavers used to interleave the sub-columns of each column of the matrix S * are different.

Preferably, the method as explained above also comprises a step of modifying the order of appearance of the columns of S *.

The invention relates in a second aspect to a method of permutation of the

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physique, représentée par un polynôme a(x)= l a, Á X 1111+1., à coefficients f-1 binaires, divisible par un premier polynôme diviseur g(x)=1+ Ig/x' + x', à l=1 coefficients binaires, fournissant une nouvelle séquence de symboles binaires

représentée par un polynôme a*(x)= Ia ,I. X5'", divisible par un second l-1 polynôme diviseur g*(x)= 1+#g *, x' + x',

caractérisé en ce que S*,k est l'élément en position U,k) dans la matrice S* obtenue selon un procédé tel qu'exposé ci-dessus, et m est un multiple du plus petit entier m'tel que le premier polynôme diviseur g(x) divise xm'+1. symbols of a binary data sequence, representative of a quantity

physical, represented by a polynomial a (x) = la, Á X 1111 + 1., with binary coefficients f-1, divisible by a first divisor polynomial g (x) = 1 + Ig / x '+ x', at l = 1 binary coefficients, providing a new sequence of binary symbols

represented by a polynomial a * (x) = Ia, I. X5 '", divisible by a second l-1 divisor polynomial g * (x) = 1 + # g *, x' + x ',

characterized in that S *, k is the element in position U, k) in the matrix S * obtained according to a method as explained above, and m is a multiple of the smallest integer m'tel than the first divisor polynomial g (x) divides xm '+ 1.

According to a preferred implementation, the first divisor polynomial g (x) is equal to the second divisor polynomial g * (x)
The invention relates in a third aspect to a coding method characterized in that it comprises an operation of determining a sequence a *, during which at least one permutation method as described above is implemented. above.

g(x) = 1 + Ig,x' + x' , un second polynôme diviseur g*(x) compatible avec g(x), @=1 un premier polynôme multiplicatif fi(x) et un deuxième polynôme multiplicatif f2(x), un nombre entier r#1, un nombre entier m multiple du plus petit entier m' tel que le premier polynôme g(x) divise xm'+1, est caractérisé en ce qu'il comporte : - une opération de constitution d'une "première" séquence, dite "séquence a" représentée par un polynôme a(x) dit "premier polynôme" dont les r.m-t premiers coefficients d'ordre croissant sont les données binaires à coder et dont les t derniers coefficients sont choisis de telle manière que le polynôme g(x) divise le polynôme a(x) In a preferred implementation, the coding method as explained, working on sequences of binary data u representative of information and taking into account a first divider polynomial @ -1

g (x) = 1 + Ig, x '+ x', a second divisor polynomial g * (x) compatible with g (x), @ = 1 a first multiplicative polynomial fi (x) and a second multiplicative polynomial f2 (x ), an integer r # 1, an integer m multiple of the smallest integer m 'such that the first polynomial g (x) divides xm' + 1, is characterized in that it comprises: - a constitution operation d 'a "first" sequence, called "sequence a" represented by a polynomial a (x) called "first polynomial" whose rm-t first coefficients of increasing order are the binary data to be coded and whose t last coefficients are chosen such that the polynomial g (x) divides the polynomial a (x)

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- an operation of constituting a second sequence called "sequence b" represented by a polynomial b (x) equal to the product of the first polynomial a (x) by the first multiplicative polynomial f1 (x), the whole divided by the first polynomial divider g (x), - a permutation operation, working on binary data of the first sequence a to form a so-called "permuted" sequence a * represented by a so-called "permuted" polynomial a * (x), whose coefficients d 'ascending order are the binary data of the permuted sequence a *, and which is divisible by the second divisor polynomial g * (x), - an operation of constituting a third sequence called "sequence c" represented by a polynomial c ( x) equal to the product of the permuted polynomial a * (x) by the second multiplicative polynomial f2 (x), the whole divided by the second divisor polynomial g * (x).

The invention also relates in a fourth aspect to a decoding method, characterized in that it implements at least one permutation created by a method according to the preceding description.

According to particular arrangements for implementing these methods, possibly used in conjunction, - the initial matrix S comprises 2401 elements and is divided into 7 columns of 343 rows, each of these 7 columns being itself divided into 7 sub- columns of 49 elements.

- the alphabet on which the turbocode is defined contains q letters, with q a power of a prime number, the alphabet receiving the structure of the Galois field with q elements.

In summary, it will be understood that by the simultaneous use of three different techniques, it is possible to design efficient interleavers for a turbocoder.

The first of these techniques is the use of small local interleavers called lock interleavers.

The second technique modifies in each column the position of the data blocks swapped locally by the latch interleavers.

The third technique is a specific method for choosing the

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different lock interleavers used for each column in the design of the overall interleaver.

The global interleavers obtained also verify a property called "return to zero" in the remainder of the description. This means that when the two elementary convolutional encoders of the turbocoder are in the zero state at the start of the encoding of an information sequence, they will both be simultaneously in the zero state at the end of the encoding of each information sequence. .

1-1 (également dit polynôme diviseur) g(x)=1+g,x + x' du turbocodeur, par ,I simple ajout de bits bien choisis en nombre égal au degré du polynôme g(x), à la fin d'une séquence d'entrée u(x). Soit a*(x) la représentation polynomiale de la séquence a(x) entrelacée. More precisely, during turbocoding, we construct a sequence whose polynomial representation a (x) is divisible by a feedback polynomial

1-1 (also called divisor polynomial) g (x) = 1 + g, x + x 'of the turbocoder, by, I simple addition of well-chosen bits in number equal to the degree of the polynomial g (x), at the end of d 'an input sequence u (x). Let a * (x) be the polynomial representation of the interlaced sequence a (x).

g(x)=(x - x, ) est la factorisation complète de g(x) dans un corps d'extension du corps à deux éléments, alors la factorisation complète de g*(x) est

(x - x, 'l) ou <P est un automorphisme (noté exponentiellement) dudit corps d'extension. Dans la suite un tel polynôme g*(x) sera dit compatible avec g(x). En particulier un polynôme est toujours compatible avec lui-même. On remarquera que deux polynômes compatibles ont le même degré. De plus, si m est le plus petit entier tel que le premier polynôme diviseur g(x) divise xm+1, et si m* est le plus petit entier tel que le second polynôme diviseur g*(x) divise We say that an interleaver satisfies the return to zero property (RZ) if, whenever a (x) is divisible by g (x), the corresponding polynomial a * (x) is also divisible by g (x) . More generally, we consider the case where the two feedback polynomials noted g (x) and g * (x) (also called first and second divider polynomials) are not necessarily equal. We then say that an interleaver satisfies the property RZ if, each time a (x) is divisible by g (x), the corresponding polynomial a * (x) is divisible by g * (x). However, this last definition only makes sense if g (x) and g * (x) have the following property: if

g (x) = (x - x,) is the full factorization of g (x) in an extension field of the two-element field, then the full factorization of g * (x) is

(x - x, 'l) where <P is an automorphism (denoted exponentially) of said extension field. In the following, such a polynomial g * (x) will be said to be compatible with g (x). In particular, a polynomial is always compatible with itself. Note that two compatible polynomials have the same degree. Moreover, if m is the smallest integer such that the first divisor polynomial g (x) divides xm + 1, and if m * is the smallest integer such that the second divisor polynomial g * (x) divides

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Considérons par exemple la factorisation g(x)=(x-a)(x-a')(x-a4) de g(x)= x3+x+1 où a est une racine primitive septième de l'unité et appartient au corps

contenant huit éléments. Considérons les six automorphismes (p, : a-3a' de ce corps à huit éléments. xm * + 1, g * (x) can only be compatible with g (x) if m = m *.

Consider for example the factorization g (x) = (xa) (x-a ') (x-a4) of g (x) = x3 + x + 1 where a is a primitive seventh root of unity and belongs to the field

containing eight elements. Consider the six automorphisms (p,: a-3a 'of this eight-element field.

We check that ci, 2 and ((J4 produce g * (x) = g (x) while ((J3, CP6 and 5 produce g * (x) = x3 + xz + I which is factored as g * (x ) = (xd) (x-a6) (xd).

The invention also relates to a device employing an interlacing and deinterlacing method such as those briefly presented above.

The invention also relates to a data transmission device comprising a transmitter suitable for implementing a packet transmission protocol, comprising a device as explained above.
In a particular embodiment, the data transmission device is such that said protocol is the ATM protocol, Asynchronous Transfer Mode.

In another embodiment, the protocol is Internet Protocol (IP).

The invention is more generally aimed at a telephone, a photographic apparatus, a printer, a scanner, a camera, a computer, a fax machine, a television set, an audio / video player, characterized in that these devices include a device as described above. briefly above.

The invention also relates to an information storage means and a removable information storage means, partially or totally, readable by a computer or a microprocessor retaining instructions of a computer program, allowing the implementation of the disclosed method. succinctly above
The description and the drawings which follow will make it possible to better understand the aims and advantages of the invention. It is clear that this description is given by way of example, and is not limiting in nature. In the drawings: FIG. 1 is a functional diagram of a turbocoder using an interleaver capable of having the RZ property;

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FIG. 2 is a table of the weights of encoded homogeneous sequences (a b c) as a function of the overall scope of the simplified sequence v; - Figure 3 shows a division of a matrix A into 49 sub-columns A112; FIG. 4 is a table of 28 septuples h with ho = 0 and h1 = 1; FIG. 5 is a representation of the matrix A; FIG. 6 illustrates a permutation of the sub-columns of the matrix A; FIG. 7 illustrates a more efficient permutation of the sub-columns of the matrix A; FIG. 8 illustrates a simplified representation of a permutation of the sub-columns of another matrix A; FIG. 9 shows bit error rate (BER) curves after decoding as a function of the signal to noise ratio (Eb / No) expressed in decibels, for four different numbers of decoding iterations; - Figure 10 shows, schematically, an encoding device suitable for implementing the preferred embodiment of the present invention, - Figure 11 is a functional diagram of a conventional turbodecoder - Figure 12 shows, schematically, a device decoding device adapted to implement the preferred embodiment of the present invention, - figure 13 represents an operating flowchart of the encoding device illustrated in figure 10, - figure 14 represents an operating flowchart of the decoding device illustrated in figure 12.

Before describing a particular embodiment of the present invention, we give below a mathematical presentation of its operation, explained in examples.

A rate 1/3 turbocoder is characterized by four polynomials: g (x) and g * (x) (called feedback polynomials), fi (x) and f2 (x), a frame length n and an interleaver. Figure 1 illustrates a rate 1/3 turbocoder.

An incoming information u (x) is coded in three sequences:

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a first sequence a (x) is the initial sequence u (x) completed by addition bits (so-called padding operation) to ensure the divisibility of the sequence completed by the feedback polynomial g (x).

- a second sequence b (x) = a (x) .f1 (x) / g (x). These first two sequences are obtained at the output of a first elementary coder 102.

- a third sequence c (x) = a * (x) .f2 (x) lg * (x) where a * (x) is the polynomial description of the interlaced version of a (x), and where g * (x ) must then check the conditions of factorization as mentioned above.

The second sequence b (x) encoded by the first elementary encoder 102 is obtained in a shift register performing a multiplication by f1 and a division by the first feedback polynomial g used in the turbocode.

The degree of f1 is often 2.3 or 4 to facilitate the design of the decoder.

The calculation of the third sequence c (x) obtained at the output of a second elementary encoder 103, first uses an interleaver 101 which mixes the coefficients of the sequence a to produce an interlaced sequence a *, as well as a shift register performing a multiplication by f2 and a division by the second feedback polynomial g *. At the output of the second elementary encoder 103, a sequence c = a * .f2 / g * is obtained. Likewise, it is generally desired that f2 be of degree 2, 3 or 4, otherwise the decoding is more and more complex.

So that c (x) is of finite length, we use an interleaver guaranteeing the return to zero, as defined above.

As we said above, an interleaver which guarantees that for any polynomial a (x) divisible by g (x), the interlaced polynomial corresponding to a * (x) is also divisible by g * (x) is called an interleaver RZ (Return to Zero).

The aim of the present invention is to provide a method of constructing RZ interleavers producing turbocodes having a good minimum distance. Suppose first that g (x) = g * (x).

We will first describe here the class of interleavers which preserves after interleaving the divisibility of a sequence a (x) by the polynomial g (x).

Next, the conditions which are involved in the construction of the interleavers according to the present invention will be presented. Finally, these elements will be combined to produce an effective interleaver.

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It is, among other things, to give all the information bits of a frame an equal or approximately equal probability of error after decoding that we choose to construct RZ interleavers.

It can be shown that an interleaver guarantees that any polynomial a (x) divisible by g (x) is such that the interlaced polynomial corresponding a * (x) is also divisible by g (x) if it can be expressed in the following way :
1. The number n of binary characters on which it acts is a multiple of m (smallest integer such that the polynomial g (x) divides the polynomial 1 + xm). To do this, we complete the sequence a (x) by zeros to reach an acceptable length n.

a=y" ax' la matrice A de taille r. m (r lignes et m colonnes) dont l'élément

en position (j,k), 0 <j <ru et 0 <k <m-1 est jazz
3. A partir de A on construit la matrice A* en appliquant à A une combinaison quelconque de permutations des deux types suivants : - une permutation quelconque agissant dans une quelconque des m colonnes de la matrice A, - une permutation des colonnes entre elles, cette permutation étant un automorphisme du code cyclique linéaire de longueur m et de polynôme générateur g. 2. Assuming then n = rm, we associate with each sequence

a = y "ax 'the matrix A of size r. m (r rows and m columns) whose element

in position (j, k), 0 <j <ru and 0 <k <m-1 is jazz
3. From A we construct the matrix A * by applying to A any combination of permutations of the two following types: - any permutation acting in any one of the m columns of the matrix A, - a permutation of the columns between them, this permutation being an automorphism of the linear cyclic code of length m and of generator polynomial g.

This permutation must therefore transform any code word of this cyclic code into a word of this cyclic code.

4. Let a * j, k be the element in position (j, k) of the matrix A * thus obtained. The interlaced version a * (x) of a (x) is defined by:

In general, an interleaving procedure replacing a (x) by a * (x) (or in an equivalent way A by A *) can be expressed in a compact way by a matrix S * of type rm whose set of all elements s * j, k (where j is the row index and k the column index) is the set of all integers from 0 to rm- 1. Two interpretations are possible to specify an interleaver from S. The first is to define the interlaced sequence a * (x) by

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Et la seconde est de définir a*(x) par

And the second is to define a * (x) by

- soit (ro,...,(m-1) le m-uple de ces résidus; ce m-uple doit être obtenu à partir du m-uple (0,1,...,m-1) par action d'une permutation qui est dans le groupe d'automorphisme du code cyclique binaire de longueur m et de polynôme générateur g(x); - il n'y a pas de restrictions sur l'ordre des éléments d'une colonne de S*. We can verify that if one of these two interleavers is of the RZ type then the other is also. The conditions given above for an interleaver to be of type RZ are then expressed as follows in terms of properties of the matrix S *: - the residue modulo m of the elements of an unspecified column of S * is constant,

- let (ro, ..., (m-1) be the m-tuple of these residuals; this m-tuple must be obtained from the m-tuple (0,1, ..., m-1) per action of a permutation which is in the automorphism group of the binary cyclic code of length m and of the generator polynomial g (x); - there are no restrictions on the order of the elements of a column of S * .

Among the two interpretations of the matrix S * given above, it is the second which has our preference.

More generally, as we said above, the interleaver can transform any a (x) multiple of g (x) into an a * (x) multiple of g * (x) when g * (x) is compatible with g (x). The representation by the matrix S * of such an interleaver is similar to what has just been said but the conditions to be satisfied by S * are slightly different: the m-uple (ro, ..., rm-1) must be now obtained from the m-tuple (0, ..., m-1) by the action of a permutation which transforms the binary cyclic code of length m and generator polynomial g (x) into the binary cyclic code of length m and generator polynomial g * (x).

The remainder of the discussion is made by supposing that g (x) = g * (x), but we can of course adapt it to the case where these two polynomials are obtained from each other by the action of a body automorphism as explained above.

In the case of g (x) = g * (x) we can also apply a modification of the order in which the columns of S * appear, provided that this permutation is an automorphism of the cyclic code of length m generated

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by g (x).

We introduce here the notion of polynomial scope (in English "span"), as well as of total scope (in English "full span").

non nuls a( =,,', 1={i1, r2, ...,r2s, Ir<lr+1, la portée sp(a) est définie comme la somme des entiers ir avec r pair, diminuée de la somme des entiers ir avec r

impair: spray = (i2-il) + (l4-!3J+...+(!2s-!2s-,)
Ce polynôme a(x) étant alors transformé par la seconde méthode décrite plus haut en polynôme a*(x), la portée sp(a*) est calculée de façon identique. Given a polynomial a (x) comprising an even number of coefficients

nonzero a (= ,, ', 1 = {i1, r2, ..., r2s, Ir <lr + 1, the scope sp (a) is defined as the sum of the integers ir with r even, reduced by the sum integers ir with r

odd: spray = (i2-il) + (l4-! 3J + ... + (! 2s-! 2s-,)
This polynomial a (x) then being transformed by the second method described above into a polynomial a * (x), the range sp (a *) is calculated in an identical way.

We then define the total scope fsp (a) as the sum of the scope of a and the scope of a *.

Suppose then a return-to-zero type interleaver defined by a matrix S * with the second of the two interpretations mentioned above, and consider a sequence a (x) = # i # lx 'whose non-zero elements are all in the same column k of matrix A (all i have the same remainder k in their division by the number m of columns in A).

In this case, such a sequence a (x) is said to be homogeneous, and is divisible by g (x) if and only if it contains an even number of non-zero elements.

est un polynôme en x"' : v(x') = a(x)/ /
Le polynôme v(x) sera appelé la version simplifiée de a(x). De façon semblable, il existe k* dans 0, ...,m-1} tel que a*(x) est divisible par xk* et que a*(x)l xk* est un polynôme en xm: v*(xm)= a*(x)l xk*. Le polynôme v* (x) appelé la version simplifiée de a*(x). We can easily understand that a (x) is divisible by xk, and that a (x) / xk

is a polynomial at x "': v (x') = a (x) / /
The polynomial v (x) will be called the simplified version of a (x). Similarly, there exists k * in 0, ..., m-1} such that a * (x) is divisible by xk * and that a * (x) l xk * is a polynomial in xm: v * ( xm) = a * (x) l xk *. The polynomial v * (x) called the simplified version of a * (x).

We can then establish that if a (x) is a homogeneous sequence, the knowledge of the total range fsp (v) of the corresponding simplified sequence, makes it possible to determine the weight of the coded sequence (a, b, c) obtained from the sequence a, when m is equal to 2t-1 where t is the degree of g (x).

For example, with g (x) = 1 + x2 + x3 (which implies m = 7), f (x) = 1 + x + x2 + x3, f2 (x) = 1 + x + x3, for a ( x) homogeneous sequence of weight 2, the weight of the coded sequence (a (x), b (x), c (x)) is always 4.fsp (v) + 6.

More generally, if a (x) is a homogeneous sequence comprising a

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an even number equal to w, of non-zero elements, and if v (x) is the associated simplified polynomial, with fi (x), f2 (x) and g (x) as previously defined, the weight of the coded sequence corresponding is equal to 4 fsp (v) + 3.w.

Moreover, it is clear that a lower limit exists for the total scope fsp (v). It is equal to the Hamming weight of the polynomial v (x) (equal to the weight of a (x))
It is then possible from these remarks to constitute a table providing for various Hamming weights of the homogeneous sequence a (noted
WH (a)) the Hamming weights WH (a, b, c) of the coded sequences (abc) as a function of the total scope fsp (v) (see FIG. 2).

By way of example, as can be seen in FIG. 2, if WH (a) is equal to 2 and if a minimum distance at least equal to 34 is desired, it is essential that the corresponding simplified sequence v have a total range fsp (v) at least equal to 7. On the other hand, if the Hamming weight WH (a) of the sequence a, is 6, the condition of having a minimum distance at least equal to 34 does not produce any additional condition on the total range, this distance condition then always being fulfilled.

Starting from a matrix A of type (r, m) associated with a sequence a (x) chosen multiple of a polynomial g (x) divider of xm + 1, each column of A is split into l sub-columns denoted Al1l2 (see FIG. 3) and called "column sub-sequences".

In order to use on each sub-column thus determined a lock interleaver, as defined previously, it is necessary that the value r / l is not a prime number (otherwise it is not possible to represent this sequence under form a matrix with at least two rows and two columns). We can therefore write r / l = N.M with M> 2. In addition, it will be seen later that the interleaver synthesis methods according to the present invention require N # M.

io, io+m, io+2m, ..., io+m(r-/)// avec io= li (m rli) +/2. Pour conserver des notations raisonnables, nous représenterons toute By nature the coefficients a, of a sub-column Al1l2 will have as indices:

io, io + m, io + 2m, ..., io + m (r - /) // with io = li (m rli) + / 2. To maintain reasonable ratings, we will represent any

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( /1-1 telle sous séquence colonne par y(x) = 2=Ca,o;/II, )xl ou, en posant y=a,O+mi, par Il) /\Ili 1 - y(x) ~ y, x' avec et rll=NM ,-il
On associe alors à l'ensemble de toutes les telles séquences y(x) une matrice Z à N lignes et M colonnes qui jouera le même rôle pour les entrelaceurs "microscopiques" que la matrice S pour l'entrelaceur "macroscopique". L'action d'un entrelaceur microscopique sur l'ensemble des séquences y(x) est représenté par une autre matrice Z*, à N lignes et M colonnes. Cette matrice Z* joue le même rôle pour les entrelaceurs microscopiques que la matrice S* pour les entrelaceurs macroscopiques.

(/ 1-1 such sub-sequence column by y (x) = 2 = Ca, o; / II,) xl or, by setting y = a, O + mi, by Il) / \ Ili 1 - y (x) ~ y, x 'with and rll = NM, -il
We then associate with the set of all such sequences y (x) a matrix Z with N rows and M columns which will play the same role for the “microscopic” interleavers as the matrix S for the “macroscopic” interleaver. The action of a microscopic interleaver on the set of sequences y (x) is represented by another matrix Z *, with N rows and M columns. This Z * matrix plays the same role for the microscopic interleavers as the S * matrix for the macroscopic interleavers.

It should be noted that these microscopic interleavers do not have to ensure a "Return to Zero" of any kind, since the condition of divisibility is to be checked at the level of the macroscopic interleaver. However, one chooses to restrict the permutations Z # Z * to those obtained by carrying out a circular permutation in each column of Z. Such a microscopic interleaver is called for the remainder of the description a lock interleaver (by analogy with the locks at rotation of parallel numbered rings).

Due to the nature of a circular permutation, such a matrix Z * (and therefore the interleaver lock associated with Z and Z *) is completely defined by the knowledge of the amplitude of the permutation carried out in each column.

A latch interleaver can therefore be defined by an M-tuple h = (ho, ..., hM-1) comprising the amplitude values of the downward circular permutation performed in each column of Z to obtain Z *.

It will be recalled in the following that this type of lock interleaver will be used to interleave (permute) elements of a column sub-sequence of A.

Given the way in which the number of columns of A was chosen, the Return to Zero (RZ) property of the resulting macroscopic interleaver will be provided in addition. As we said above, this property RZ remains ensured if a modification of the order in which the columns of A appear on the condition that this modification is an automorphism of the cyclic code of length m and of generator polynomial g ( x).

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This technique is the first of the three techniques mentioned above for producing efficient interleavers.

For example, in the case N = M = 7, which corresponds to column subsequences of length 49 (having 49 elements), to allow the generated turbocode a minimum distance equal to 34, it is necessary that each microscopic interleaver Z # Z * guarantees that fsp (y) is greater than or equal to 7, for each simplified sequence y of Hamming weight equal to 2, and a total range fsp (y) greater than or equal to 6 for each simplified sequence of Hamming weight equal to 4.

With N # M # 2, we can show that any lock interleaver Z # Z * of size NM described by an M-tuple h as defined above, has the property that all the simplified sequences y (x) of Hamming weight equal to 2 have their total range fsp (y) greater than or equal to the value M as soon as the M elements of h are of different value (which amounts to saying that one must apply circular permutations of different values to all the columns of the matrix representation of the column subsequence).

Returning then to the case N = M = 7, we have a priori 77 possible combinations of circular permutations on the 7 columns, but in fact only 7 !, i.e. 5040 satisfy the condition fsp (y) greater than or equal to 7 for each simplified sequence y (x) of weight 2.

2,1, 0, ..., 0]' et la première colonne de T2 est [2,-2,0, ...,0]', on peut démontrer la propriété suivante : avec N > M # 6, tout entrelaceur verrou Z#Z* de taille NM décrit par un M-uple h tel que défini plus haut, a la propriété que toutes les séquences simplifiées y(x) de poids de Hamming égal à 4 ont leur portée totale fsp(y) supérieure ou égale à la valeur 6 dès que les restes modulo N de hT1 et de hT2 ne contiennent pas de composante nulle. Assuming then that T1 and T2 are two circulating matrices (matrix of which each column is deduced from the preceding one by shifting (rotation) of a notch downwards) of type M x M, such as the first column of T! is [1, -

2,1, 0, ..., 0] 'and the first column of T2 is [2, -2,0, ..., 0]', we can prove the following property: with N> M # 6, any interleaver lock Z # Z * of size NM described by an M-tuple h as defined above, has the property that all the simplified sequences y (x) of Hamming weight equal to 4 have their total scope fsp (y) greater than or equal to the value 6 as soon as the modulo N remainders of hT1 and hT2 do not contain a zero component.

Returning again to the case N = M = 7, we can determine the seven times h satisfying both the previous properties. For example for a first zero component (no circular permutation of the first

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column), we have exactly 168 septuples satisfying these properties.

For the case where moreover h1 = 1 (circular permutation of amplitude equal to one of the second column), we have 28 such septuples satisfying the two properties (see the table of figure 4).

h()=(0643 25), h(2)=(051 6243), h(3) =(0 45236 1) h(4)=(0 3 2 5 4 1 6), h(5)=(0 2 6 1 5 3 4), h(6)=(0 1 3 4 6 5 2) ce dernier septuple étant le dernier élément de la figure 4. For example, it is shown that the following septuples satisfy the stated conditions:

h () = (0643 25), h (2) = (051 6243), h (3) = (0 45236 1) h (4) = (0 3 2 5 4 1 6), h (5) = ( 0 2 6 1 5 3 4), h (6) = (0 1 3 4 6 5 2) this last sevenfold being the last element of figure 4.

In another example (with M = 5), if one wishes to obtain a turbocode having a minimum distance of 42, one sees on the table of figure 2 that this implies that for sequences y of weight 2, the total range fsp (y) is greater than or equal to 9 and for sequences of weight 4, the total range fsp (y) is greater than or equal to 8. We also notice that the condition fsp (y) # 42 is always verified for the sequences of weight 6 or more.

We then seek to construct interlacers Z # Z * where Z and Z * are matrices with N rows and 5 columns. We must therefore specify interleavers with 5-uples h = [ho, h1, h2, h3, h4] of numbers h, between 0 and N-1 (limits included), such as the total scope fsp (y) of any simplified sequence y (x) of weight 2 is greater than or equal to 9 and that the total range fsp (y) of any simplified sequence y (x) of weight 4 is greater than or equal to 8 (see figure 2).

We can check that this is done for all the sequences y (x) of weight 2, if and only if any two components h ,, h, of h are such that their modulo N difference is in absolute value greater than 1 (nor zero, neither -1, nor 1).

To check the condition for all the sequences of weight 4, we can highlight some conditions necessary to be fulfilled by the m-uples h already fulfilling the condition for the sequences of weight 2, and restricting ourselves to the case where the first component ho is zero (no circular permutation of the first column of Z to obtain the first column of Z *).

Let us suppose in fact that T1, T2, ... T7 are seven circulating matrices of

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[1, -2, 1, 0, 07', pour T2:[2, -2, 0, 0, 0]\ pour T3 : [2, -1, -1, 0, 0]', pour T4 : [1, -1, -1, 1, 0]', pour T5 : [1, 1, -2, 0, 0]', pour T6.- [1, 0, -2, 1, 07', pour T7 : [1, -2, 0, 1, 0] '. type M x M, comprising respectively as first columns, for T1

[1, -2, 1, 0, 07 ', for T2: [2, -2, 0, 0, 0] \ for T3: [2, -1, -1, 0, 0]', for T4: [1, -1, -1, 1, 0] ', for T5: [1, 1, -2, 0, 0]', for T6.- [1, 0, -2, 1, 07 ', for T7: [1, -2, 0, 1, 0] '.

A first necessary condition is that for i = 1 to 7, the modulo N remainder of hT, does not have a component equal to 0.1 or −1.

By introducing a circulating matrix 5 x 5 T8 of the first column [1, 1, - 1, -1, 0] ', a second necessary condition is that the modulo N remainder of hT8 does not have a component equal to 1 or- 1.

By introducing a circulating matrix 5 x 5 T9 of the first column [1, -1, 1, -1, 0] ', a third necessary condition is that the remainder modulo N of hTg does not have a component equal to 0 or 1 .

It is then verified that for N = 26, these (necessary) conditions are also sufficient and that for N equal or less than 25 these conditions are never satisfied.

For N = 26, there are 120 quintuples satisfying the stated conditions.

These quintuples are all modulo 26 non-zero multiples of the following 10 quintuples:
0 2 6 22 8
0 2 8 20 16
0 2 10 16 12
0 2 10 22 6
0 2 12 8 20
0 2 16 12 18
0 2 18 14 6
0 2 20 6 22
0 2 22 6 18
0 2 22 14 10
A method for constructing microscopic interleavers satisfying the necessary conditions allowing the minimum distance from the turbocode generated by the associated macroscopic interleaver to be greater than a predetermined value has been explained in the preceding pages.

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séquences de très faible poids. En effet, avec g(x)=1+x2+x3, f1(x) = 1 +x++)(3 et f2(x)=1+x+x3 tels que considérés plus haut, un polynôme de la forme a(x)=x7'.g(x) vérifie a*(x) =x7j.g(x), pour un certain j. En conséquence, le poids de Hamming correspondant à la séquence encodée (a, b, c) est seulement de 10, ce qui est une valeur assez faible. By then based on the lock interleavers defined above for the sub-columns A112, it is assumed here that an identical lock interleaver Z # Z * is used for all the sub-columns. In this case, the global interleaver is such that the corresponding turbocode contains a fairly large number of

very low weight sequences. Indeed, with g (x) = 1 + x2 + x3, f1 (x) = 1 + x ++) (3 and f2 (x) = 1 + x + x3 as considered above, a polynomial of the form a ( x) = x7'.g (x) satisfies a * (x) = x7j.g (x), for some j. Consequently, the Hamming weight corresponding to the encoded sequence (a, b, c) is only of 10, which is a fairly low value.

We define here the notion of scope sp (a) and total scope fsp (a) for trinomials a (x) = xi + xj + Xk with i <j <k by the following values: sp (a) = ki, and fsp (a) = spray + sp (a *).

Following the action of a latch interleaver on each of the Al1l2 sub-columns, a matrix A * is obtained. As each sub-column Al1l2 permuted by a latch interleaver preserves until now the same relative position in A * as in A, this matrix A * is still represented by the same table, for example that given in figure 5, as the matrix A.

In order to avoid certain coded sequences of low weight such as those of weight 10 mentioned above, the matrix A * obtained hitherto obtained will also be modified by interchanging the sub-columns of the same column with each other.

It can then be shown on examples that all the permutations permuting the sub-columns of each column with each other are not equivalent in terms of minimum distance from the turbocode obtained.

a(x)=x7'.g(x), a*(x) =x 7j. g(x), mentionnée ci-dessus, toute situation du type a(x)=(x'+x'+x').g(x) et a*(x)=(x'*+x'*+xk*).g(x) car le poids de la séquence codée correspondante est égal à 30, et donc strictement inférieur à 34, qui est la distance minimale souhaitée. In particular, it is observed that it is desirable to avoid, in addition to the situation

a (x) = x7'.g (x), a * (x) = x 7j. g (x), mentioned above, any situation of the type a (x) = (x '+ x' + x '). g (x) and a * (x) = (x' * + x '* + xk *). g (x) because the weight of the corresponding coded sequence is equal to 30, and therefore strictly less than 34, which is the desired minimum distance.

A permutation of the sub-columns of A * which avoids the first of the unfavorable situations which have just been evoked is represented in figure 6. The presence in figure 6 of the pair (il, l2) in the position occupied at the

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position initiale de (A *)5', la sous-colonne (A *) 2 est déplacée dans la position initiale de (A*)32, la sous-colonne (A*)03 est déplacée dans la position initiale de (A*)3', ..., , la sous-colonne (A*)10 reste où elle est, ..., , la sous-colonne (A*)66 est déplacée dans la position initiale de (A*)16. figure 5 by the pair (k1, k2) means that the sub-column (A *) k1k2 is moved to the position previously occupied by the sub-column (A *) l1l2. In particular, in the example given, the sub-column (A *) 01 is moved into the

initial position of (A *) 5 ', the sub-column (A *) 2 is moved to the initial position of (A *) 32, the sub-column (A *) 03 is moved to the initial position of (A *) 3 ', ...,, the sub-column (A *) 10 remains where it is, ...,, the sub-column (A *) 66 is moved to the initial position of (A *) 16 .

f2(x) comme ci-dessus, la séquence a(x=(x3l+'+xs'+j+xGl).g(x) produit a*(x)=(>?+yr+2+x6r).g(X), et on vérifie que la séquence codée correspondante à un poids de 30. However, this permutation has the drawback of not avoiding the second unfavorable situation mentioned above. Indeed, with q = rll, g (x), fi (x), and

f2 (x) as above, the sequence a (x = (x3l + '+ xs' + j + xGl) .g (x) produces a * (x) = (>? + yr + 2 + x6r) .g (X), and it is verified that the coded sequence corresponding to a weight of 30.

Let us consider, on the contrary, the permutation of the sub-columns of A * among themselves which is given in FIG. 7. In this case the second unfavorable situation mentioned above is also avoided. Consequently the global interleaver induced by Figure 7 eliminates from the code many sequences of weight # 30 and replaces them with sequences of weight # 34.

Here are some details on how to find permutations that have this effect. For this purpose we simplify and generalize the representations of figures 5,6 and 7. As a simplification we omit the second number l2 in each pair l1, l2, because the value of l2 is not modified by the permutations that we consider. As a generalization, we accept that q can be strictly greater than the number of columns. With these two conventions and q = 8, a permutation of the sub-columns between them which has the desired effect is given in figure 8.

est impossible de trouver 9 paires (it, jt), (ir, lr+2) (lr jt+3) pour t compris entre 1 et 3, où les ir et les jr, sont des nombres entiers satisfaisant 0 S it s q-1 et 0 s h s 6 et où les additions se font modulo 7, telles que lorsque ces paires sont considérées comme les indices de ligne et de colonne des éléments de la matrice donnée à la figure 8, il y a exactement trois entiers différents We can then prove the following property:
The second adverse situation mentioned above is avoided if it

is impossible to find 9 pairs (it, jt), (ir, lr + 2) (lr jt + 3) for t between 1 and 3, where the ir and the jr, are integers satisfying 0 S it s q -1 and 0 shs 6 and where the additions are made modulo 7, such that when these pairs are considered as the row and column indices of the elements of the matrix given in figure 8, there are exactly three different integers

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each appearing in three of the nine positions thus obtained. The matrix represented in FIG. 8 clearly avoids this unfavorable situation as can be verified by a program in MATLAB language provided in the appendix.

In order to further improve the turbocode, we choose to use a different latch interleaver for each column of A.

Consider the case where each sub-column A112 contains 49 elements, where A contains 7 columns and where each column contains 7 sub-columns. The length of the corresponding sequence a (x) is therefore equal to 49 x 7 x 7 = 2401.

We choose to build the matrix A * by permuting the sub-columns of each column between them according to the rule shown in figure 7.

h 1, h2 h3, ha h5, /le]-
Le choix de l'entrelaceur verrou associé à chaque sous colonne est réalisé comme suit :
On numérote de 0 à 6 les colonnes de A et A*, et on utilise les septuples suivants :

h(1)=(06431 25), h(2)=(051 6243), h(3)=(0 4 5 2 3 6 1) h(4)=(0 3 2 5 4 16), h(5) =(0 2 6 1 5 3 4), h(6)=(0 1 3 4 6 5 2). Then, to each sub-column Al1l2 of 49 elements having a fixed value of l2, we associate the same interleaver lock 7 x 7 specified by a sevenfold h = [ho,

h 1, h2 h3, ha h5, / le] -
The choice of the interleaver lock associated with each sub column is carried out as follows:
We number from 0 to 6 the columns of A and A *, and we use the following septuples:

h (1) = (06431 25), h (2) = (051 6243), h (3) = (0 4 5 2 3 6 1) h (4) = (0 3 2 5 4 16), h ( 5) = (0 2 6 1 5 3 4), h (6) = (0 1 3 4 6 5 2).

Each of these septuples specifies a lock interleaver, and the lock specified by h (i) is used to swap all sub-columns in column i (i = 1, ..., 6) of A.

For the column with index 0, the sub-columns are permuted using one of the six defined septuples, for example h (1).

We saw above that these septuples satisfy the conditions necessary so that the global scope of a simplified sequence y (x) corresponding to a homogeneous sequence a (x) is greater than or equal to 7 if the Hamming weight of the sequence a (x) is equal to 2, and either greater than or equal to 6 if the Hamming weight of a (x) is equal to 4.

The reason for choosing different latch interleavers in each column of A is as follows. If we didn't, it would be possible to

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choisir pour i fixé, un nombre j tel que la séquence a(x)=x(1+x')(I+x'+2+x'+3) soit entrelacée en a*(x)=x*{l-tx7J*)(J+x:'+x?) par un entrelaceur de type décrit par la figure 7. Dans ce cas, le poids de la séquence codée correspondante pourrait être strictement inférieur à 34.

choose for fixed i, a number j such that the sequence a (x) = x (1 + x ') (I + x' + 2 + x '+ 3) is interlaced in a * (x) = x * {l -tx7J *) (J + x: '+ x?) by an interleaver of the type described in FIG. 7. In this case, the weight of the corresponding coded sequence could be strictly less than 34.

In another example, the sub-columns have a "length" of 117 elements, and are placed in 13 x 9 matrices, to be interlaced by 13 x 9 lock interleavers. The global interleaver then swaps 117 x 49 or 5733 bits. of information.

In this case, for i between 1 and 12, we denote h (i) the following 9-uple: h (i) = (O i 5i 7i 12i 8i 11 i 9i 3i) all of whose values are calculated modulo 13. Each such 9-uple completely defines a latch interleaver (we recall that it gives by each of its components the amplitude of the rotation of each column of a 9-column matrix) which satisfies a condition of global scope fsp (y )> 9 for all the sequences a of weight 2, and fsp (y)> 8 for the sequences a of weight 4, which allows to expect a minimum distance equal to 42 (see figure 2). For this, for example, different h (i) will be used in the 7 columns of A and a permutation of the columns between them will be applied of the type described in FIG. 8.

f1(x) = 1 +X+X2+X3 et f2(x)= 9+x+x3 . We thus obtain a turbocode suitable for encoding binary sequences of length 5733 and specified as said above by g (x) = 1 + x2 + x3,

f1 (x) = 1 + X + X2 + X3 and f2 (x) = 9 + x + x3.

Simulations have been carried out in the case where an interleaver of length 2401 is used (first example above). They are illustrated by FIG. 9 which gives for four different numbers of decoding iterations the error rate per bit (BER) as a function of the signal to noise ratio per bit (Eb / No expressed in dB). It can be seen that the gain is very significant for signal / noise ratios that are already low, and that most of the gain is obtained after 8 iterations.

It is clear that compared to the interleavers usually used, the interleaver proposed in the present invention offers the major advantage of guaranteeing the simultaneous return to zero of the two elementary encoders while at the same time.

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guaranteeing good code distance distribution, which is an advantageous factor when the signal to noise ratio per bit Eb / No is high.

The description of a particular embodiment of the device embodying the present invention will now continue with reference to Figures 10 to 14.

FIG. 10 schematically illustrates the constitution of a network station or computer coding station, in the form of a block diagram.

This station comprises a keypad 911, a screen 909, an external information source 910, a wireless transmitter 906, jointly connected to an input / output port 903 of a processing card 901.

The processing card 901 comprises, interconnected by an address and data bus 902: a central processing unit 900; - a random access memory RAM 904; - a non-volatile memory 905; and - the input / output port 903.

Each of the elements illustrated in FIG. 10 is well known to those skilled in the art 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 910 is, for example, an interface peripheral, a sensor, a demodulator, an external memory or another information processing system (not shown), and is preferably suitable for providing sequences of signals representative of speech, of service messages or of multimedia data, in particular of IP or ATM type, in the form of binary data sequences, - the wireless transmitter 906 is suitable for implementing a communication protocol. packet transmission over a wireless channel, and to transmit those packets over such a channel.

It is further observed that the word “register” used in the description designates, in each of the memories 904 and 905, both a low-capacity memory area (some binary data) and a memory area.

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large capacity (allowing to store an entire program).

Random access memory 904 stores data, variables and intermediate processing results in memory registers bearing, in the description, the same names as the data whose values they store. The random access memory 904 comprises in particular the following registers: - an "nb ~ data" register in which the length of the data sequence to be encoded is kept, - a register "a", in which a, the data sequence to be encoded is kept. code, including the input sequence u and the added bits (padding bits) guaranteeing the divisibility of the sequence a by g (the input sequence u not necessarily being divisible by g, the first encoder adds to the sequence input u a number of bits equal to the degree of g thus forming the sequence a to make the latter divisible by g) - a register a * in which the interlaced sequence a * is kept, - a register a, b, c in which are kept the sequences resulting from the turbo coding a, b and c, and - a register "~ radio frame" in which is stored the entire radio frame to be transmitted.

The non-volatile memory 905 is suitable for keeping, in registers which, for convenience, have the same names as the data they keep: the operating program of the central processing unit 900, in a "program" register , - the sequence g, in a register "g", - the sequence f1, in a register "f1", - the sequence f2, in a register "f2", - the size of the interleaver n, in a register n - an "interleaver" register in which is kept the table defining the interleaver, as a function of the value of n, - the value m, of the period of g in a register m
The central processing unit 900 is suitable for implementing the flowchart described in FIG. 13.

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In FIG. 11, it can be seen that a decoding device is essentially made up of: - three soft inputs 1001, 1002 and 1003 of sequences a, b and c, estimates of the coded sequences, - a first decoder 1004 corresponding to the first elementary coder 102 (figure 1) and receiving the sequences a and b as well as an extrinsic information sequence w4, initialized to zero, provides an a posteriori estimation sequence w1, - an interleaver 1005, identical to the interleaver used in the encoder , which receives the sequence w1 and the interleave in w2, - a second decoder 1006, corresponding to the second elementary coder 103 and receiving the sequences w2 and c, and provides on the one hand an a posteriori estimation sequence w3 and, d 'on the other hand, an estimated sequence a', and - a deinterleaver 1007, inverse of the interleaver 1005, receiving the sequence w3 and providing the sequence w4.

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

In accordance with the present invention, the decoders 1004 and 1006 are initialized taking into account the fact that the elementary encoders 102 and 103 each have an initial state and a zero final state.

FIG. 12 schematically illustrates the constitution of a network station or computer coding station, in the form of a block diagram.

This station comprises a keyboard 1111, a screen 1109, an external information recipient 1110, a wireless receiver 1106, jointly connected to an input / output port 1103 of a processing card 1101.

The processing card 1101 comprises, interconnected by an address and data bus 1102: a central processing unit 1100; a random access memory RAM 1104; - a non-volatile memory 1105; and

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- the input / output port 1103.

Each of the elements illustrated in FIG. 12 is well known to those skilled in the art 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 recipient 1110 is, for example, an interface peripheral, a display, a modulator, an external memory or another information processing system (not shown), and is preferably suitable for receiving sequences of signals representative of speech, service messages or multimedia data, in particular of IP or ATM type, in the form of binary data sequences, - the wireless receiver 1106 is suitable for implementing a transmission protocol by packets on a wireless 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 1104 and 1105, both a low-capacity memory area (some binary data) and a large-capacity memory area (making it possible to store an entire program).

Random access memory 1104 stores data, variables and intermediate processing results in memory registers bearing, in the description, the same names as the data whose values they store. The random access memory 1104 comprises in particular the following registers: - "data ~ received" registers, in which the received sequences are respectively stored, - "inf extrinsic" registers, in which the intermediate decoding sequences (see FIG. 11) are respectively stored , - an "estimated ~ data" 'register, in which the decoded sequence a' is kept, - a "nb ~ iterations" register, in which the value of the number of iterations performed by the turbo decoder is kept, - a register nb ~ data in which the length of the sequence to be decoded is kept.

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- A "radio ~ frame" register in which the entire received radio frame is stored.

- le nombre maximal d'itérations dans un registre nb-iteration-max
L'unité centrale de traitement 1100 est adaptée à mettre en #uvre l'organigramme décrit à la figure 14. The non-volatile memory 1105 is suitable for keeping, in registers which, for convenience, have the same names as the data they keep: - the operating program of the central processing unit 1100, in a "program" register , - the sequence g, in a register "g", - the sequence f1, in a register "f1", - the sequence f2, in a register "f2", - the size of the interleaver, n, in a register n, - an "interleaver" register in which is kept the table defining the interleaver and its inverse interleaver as a function of n, - the value, m, of the period of g in a register m

- the maximum number of iterations in a register nb-iteration-max
The central processing unit 1100 is adapted to implement the flowchart described in figure 14.

In FIG. 13, it is observed that, following an initialization operation 1201 of a type known to those skilled in the art of systems comprising a central unit, during an operation 1202, the central unit 900 waits for 'a sequence of symbols to be encoded is transmitted to it by the information source 910. It is observed here that the end of this sequence is marked, either by a fairly long delay before another symbol is transmitted, or by information having particular values which signify that the sequence is complete.

Then, during an operation 1203, the central unit 900 determines the number n ′ of symbols of the sequence which are to be transmitted, by extracting the symbols which are not intended to be transmitted, according to known procedures.

Then, during an operation 1204, the central unit performs a padding operation during which, at the end of the sequence of symbols

<Desc / Clms Page number 27>

to be transmitted, a number of binary symbols equal to the degree of the divisor polynomial g (x), is added so that the polynomial representation of this sequence is divisible by the polynomial g (x).

Then, in parallel: - a so-called "stuffing" operation 1205 is performed, during which binary symbols of zero value are added at the end of the sequence resulting from the padding operation, so that the number n of binary symbols of the final sequence is an admissible multiple of the number m, which is, we recall, the smallest value such that the polynomial xm + 1 is divisible by the polynomial g (x); - An interleaver 1206 choice operation is performed as a function of its length n.

Then, the sequence resulting from the stuffing operation 1205 is turbocoded during a turbocoding operation 1207 implementing the interleaver chosen during the operation 1206, the divider polynomial g (x) and the multiplier polynomials f1 (x) and f2 (x).

Then, during a stuffing bit removal operation 1208: the stuffing bits are removed at the end of the systematic sequence and of the first parity sequence to form, respectively, the sequences a and b.

Finally, during an operation 1209, the sequences a, b and c are inserted into radio frames, they modulate electromagnetic signals and are transmitted on a radio channel.

Operation 1202 is then repeated.

In FIG. 14, it is observed that, following an initialization operation 1301 of a type known to those skilled in the art of systems comprising a central unit, during an operation 1302, the central unit 1100 waits for 'a radio frame is transmitted to it by the encoding and transmission device. It is observed here that the end of this radio frame is marked by information having particular values.

Then, during an operation 1303, the central unit 1100 determines the number n and the number of symbol stuffing bits of the radio frame which

<Desc / Clms Page number 28>

are to be decoded.

Then, in parallel: - during an operation 1304, the central unit 1100 performs a "stuffing" operation on the first two sequences to be decoded, by adding to them stuffing bits and the corresponding parity bits assigned with a highest possible reliability value corresponding to a zero hard bit such that the length of the resulting sequence is equal to n, and - during an operation 1305, the central unit 1100 makes the choice of the interleaver and its inverse interleaver, taking into account the value of n, in non-volatile memory 1105.

Then, during an operation 1306, the three sequences coming, for the first two from the stuffing operation 1304 and, for the last from the operation 1303, are decoded according to turbo decoding procedures well known in the industry. skilled in the art. Here, these procedures implement the interleavers chosen during operation 1305, the divisor polynomial g (x), the multiplier polynomials f1 (x) and f2 (x), a number of iterations less than or equal to the number d 'maximum authorized iterations and an initialization of the elementary decoders taking into account the fact that the initial and final states of the encoders are harmful. This operation provides an estimate of the sequence a '.

Then, during an operation 1307, the symbols added during the stuffing operation 1304 and those coming from a padding operation performed during encoding (see operation 1204), and which are, for the latter, in number equal to the degree of the divisor polynomial g (x), are removed from the sequence a 'to form the transmitted sequence. Finally, the sequence is transmitted to the information destination 1310 and the operation 1302 is repeated.

According to a variant, the random access memory 904 (respectively 1104) is removable, partially or totally, and comprises, for example a magnetic tape, a floppy disk or a rewritable compact disc.

It is generally noted that in the interleaving method as described, the data is read row by row (in the matrix A) before and after interleaving.

It is also clear that during the practical implementation of the method

<Desc / Clms Page number 29>

interlacing (or deinterlacing), we do not necessarily go through a step of matrix formatting of the incoming data. It is possible, by using the interleaver permutation table (which associates an output position with each input position, after permutation), to work directly on the incoming data as they arrive. However, the process remains unchanged in principle.

Of course, the present invention is not limited to the details of the embodiments described here by way of example, but on the contrary extends to modifications within the reach of those skilled in the art.

In particular, it extends to the case where the alphabet on which the turbocode is defined contains q letters, with q a power of a prime number.

The alphabet can then receive the structure of the Galois field with q elements.

Likewise, the invention has been described here using two interleavers. It is clear that it applies more generally to the case of a code comprising several interleavers with feedback polynomials conforming to the description.

<Desc / Clms Page number 30>

Appendix In this appendix, we present the MATLAB program intended to avoid the second unfavorable situation mentioned above.

(i,ii), (i, ii+2), (i, ii+3) U, jj), U, jj+2), U, jj+3) (k, kk), (k, kk+2), (k, kk+3) This program tests a matrix, a, such as the one given in figure 8. This program uses a matrix called filt and a vector called zero: filt = [-110000000
0-11000000
000-110000
0000-11000
000000-110
0000000-11]; zero == [
000000] '; It first builds a matrix m by juxtaposition of a with itself: m = [aa and it initializes a parameter y to zero: y = 0; He then builds the sets of 9 pairs of indices

(i, ii), (i, ii + 2), (i, ii + 3) U, jj), U, jj + 2), U, jj + 3) (k, kk), (k, kk + 2), (k, kk + 3)

<Desc / Clms Page number 31>

and construct the 9-tuple d whose elements are the elements of the matrix m in each of the 9 positions above, from (i, ii) to (k, kk + 3):

<tb>
<tb> i = 0 <SEP>;<SEP>
<tb>

while ((y= =0)+(i<6))= =2,i=i+1 ;ii=O; while ((y= =0)+(ii<7))= =2,ii=ii+1 ;aa=[m(i,ii) m(i,ii+2)

while ((y = = 0) + (i <6)) = = 2, i = i + 1; ii = O; while ((y = = 0) + (ii <7)) = = 2, ii = ii + 1; aa = [m (i, ii) m (i, ii + 2)

<tb>
<tb> m (i, ii + 3)];
<tb> j = i <SEP>;
<tb> while <SEP> ((y = <SEP> = 0) + (j <7)) = <SEP> = <SEP> 2, j = j + 1 <SEP>; jj = O;
<tb>

while ((y= =0)+(jj<7))= = 2,jj=jj+1 ;bb=[mU,jj) mU,jj+2)

while ((y = = 0) + (jj <7)) = = 2, jj = jj + 1; bb = [mU, jj) mU, jj + 2)

<tb>
<tb> m <SEP> (d, dd + 3)];
<tb> k = j;
<tb> while <SEP> ((y == 0) + (k <8)) == 2, k = k + 1; kk = 0;
<tb>

while ((y==0)+(kk<7))==2,kk=kk+1;cc=[m(k,kk)

while ((y == 0) + (kk <7)) == 2, kk = kk + 1; cc = [m (k, kk)

for iii=1 :8,for jjj=1 +iii:9,if d(üi)>d(jjj), side=d(iii);d(iii)=d{jjj);d(jjj)=side;

<tb>
<tb> m <SEP> (k, kk + 2) <SEP> m (k, kk + 3)];
<tb> d = [aa <SEP> bb <SEP>cc];
<tb>
It reorders the 9 elements of d in ascending order:

for iii = 1: 8, for jjj = 1 + iii: 9, if d (üi)> d (jjj), side = d (iii); d (iii) = d {jjj); d (jjj) = side ;

<tb>
<tb>end;end;end;
<tb>
and it checks that the number of pairs of equal consecutive elements in d is not equal to 6.

If it is, he sets y = y + 1:

<tb>
<tb> qq = filt * d '; q = [1 <SEP> 1 <SEP> 1 <SEP> 1 <SEP> 1 <SEP>] * (qq == zero);
<tb>

if q= =6,y=y+1 ;end;

if q = = 6, y = y + 1; end;

<tb>
<tb>end;end;end;end;end;end;
<tb>
If, at the end of the calculation, y is still zero, the test is positive and the program sets m = a:

<tb>
<tb> if <SEP> y = <SEP> = 0, <SEP> m = a, <SEP>end;
<tb>

Claims (30)

1. Method for creating a permutation table, characterized in that said table matches each input rank from 0 to r.m-1 to an output rank from 0 to r.m-1, said method comprising the following steps: E1- we consider a matrix S comprising r rows and m columns, filled row by row by the successive numbers from 0 to r.m-1, E2- each column of said matrix S is split into a predetermined number / of sub-columns, such that r / l is not prime, E3- the sub-columns of S in number equal to l.m are designated by Sl1l2

with 0 sI, 1-1 and D <l2 <m-1 where 12 refers to the column of S where appears Sl1l2 and where / 1 refers to the position of the sub-column Si, 12 in the index column l2. E6- the permutation table consists of couples each formed of an element of the matrix S and of the element of the same position of the matrix S *. E5- this matrix with N rows and M columns is reconverted, after said circular permutations on its columns, into a sub-column S * l1l2 which will occupy in a matrix S * the same place as that occupied by Si, 12 in the matrix S, E4- each sub-column Si, 12 is then written in the form of a matrix with N rows and M columns (with r / l = NM) and in this form it is interlaced by an interleaver of the type called "lock" defined by a circular permutation of each column of said matrix with N rows and M columns, said interleaver not being the identity, 2. Method according to claim 1 characterized in that it also comprises in at least one column l2 (0 <l2 # m-1) of the matrix S * a modification of the order of appearance of the sub-columns S * l1l2. 3. Method according to any one of claims 1 to 2, characterized in that the same latch interleaver is used to produce each of the / sub-columns S * l1l2 of a given column l2 of the matrix S *. 4. Method according to claim 3, characterized in that the sub-columns of at least two columns of the matrix S * are produced by <Desc / Clms Page number 33> different lock interleavers. 5. Method according to claim 4, characterized in that the m lock interleavers used to produce the sub-columns of each column of the matrix S * are different. 6. Method according to any one of claims 1 to 5, characterized in that it also comprises a step of modifying the order of appearance of the columns of S *. 7. Method of permutation of the symbols of a binary data sequence, representative of a physical quantity, represented by a

polynomial a (x) = I: a l 'X 111 / +', with binary coefficients, divisible by a prime

(-1 divisor polynomial g (x) = 1 + Ig, x '+ x', with binary coefficients, providing a new sequence of binary symbols represented by a polynomial a * (x) =

(-1 "a" X5'1, divisible by a second divisor polynomial g * (x) = 1+ "g *, Xl + Xl, 1 = 1 characterized in that S * j, k is the element in position (j, k) in the matrix S * obtained according to any one of claims 1 to 6, and m is a multiple of the smallest integer m't such that the first divisor polynomial g (x) divides xm '+ 1. 8. Method of permutation of the symbols of a binary data sequence, representative of a physical quantity, represented by a

polynomial a (x) = a, x "'+ A, with binary coefficients, divisible by a first t- \ divisor polynomial g (x) = 1 + g, x' + x ', with binary coefficients, providing a new sequence of binary symbols represented by a polynomial

a * M s. x 1111+ '., divisible by a second divisor polynomial 0 </; - l to 1-1 g * (x) = 1 + g * rx' + x ', it characterized in that s * j, k is l 'element in position (j, k) in the matrix S * obtained according to any one of claims 1 to 6, and m is a multiple of the smallest integer m't such that the first divisor polynomial g (x) divides xm' + 1 . <Desc / Clms Page number 34> 9. Method according to any one of claims 7 to 8, characterized in that the second divisor polynomial g * (x) is equal to the first divisor polynomial g (x) 10. Coding method characterized in that it comprises an operation of determining a sequence a *, during which at least one permutation method according to any one of claims 7 to 9 is implemented. 11. Coding method according to claim 10, working on sequences of binary data u representative of information and taking into account

has a first divisor polynomial g (x) = 1 + g, x '+ Xl, a second, -l divisor polynomial g * (x) compatible with g (x), a first multiplicative polynomial f1 (x) and a second polynomial multiplicative f2 (x), an integer r # 1, characterized in that it comprises: - an operation of constituting a "first" sequence, called "sequence a" represented by a polynomial a (x) called "prime polynomial "whose rm-t first coefficients of increasing order are the binary data to be encoded and whose t last coefficients are chosen such that the polynomial g (x) divides the polynomial a (x) - a constitution operation d 'a second sequence called "sequence b" represented by a polynomial b (x) equal to the product of the first polynomial a (x) by the first multiplicative polynomial f1 (x), the whole divided by the first divisor polynomial g (x), - a permutation operation, working on binary data of the first sequence a to form a so-called "permuted" sequence a * represented by a poly so-called "permuted" nome a * (x), whose coefficients of increasing order are the binary data of the permuted sequence a *, and which is divisible by the second divisor polynomial g * (x), - a constitution operation d 'a third sequence called "sequence c" represented by a polynomial c (x) equal to the product of the permuted polynomial a * (x) by the second multiplicative polynomial f2 (x), the whole divided by the second divisor polynomial g * (x ). <Desc / Clms Page number 35> 12. Decoding method, characterized in that it implements at least one permutation method according to any one of claims 7 to 9. 13. Turbo-decoding method characterized in that it implements at least one permutation method according to any one of claims 7 to 9. 14. A method suitable for decoding sequences received after encoding by the encoding method according to any one of claims 10 to 11. 15. Method according to any one of claims 1 to 14 characterized in that the initial matrix S comprises 2401 elements and is divided into 7 columns of 343 rows, each of these 7 columns being itself divided into 7 sub-columns of 49 elements. 16. Method according to any one of claims 1 to 15, characterized in that the alphabet on which the turbocode is defined contains q letters, with q a power of a prime number, the alphabet receiving the structure of the body of Galois with q elements. 17. Interleaver (101) adapted to supply, from a sequence a of binary data representative of a physical quantity, associated with a

polynomial a (x) = 2:> /, Á .x / 1JI4Á divisible by a first divisor polynomial g (x), and whose coefficients of increasing order are the binary data of the sequence a, an associated permuted sequence a * to a polynomial a * (x) whose coefficients of increasing order are the binary data of the sequence a *, said polynomial a * (x) being intended to be divided by a second divisor polynomial g * (x) compatible with the first divider polynomial g (x), to form a sequence of binary data c, and a having a number of binary data equal to the product of any integer r by the integer m, m being a multiple of the smallest integer m 'such that the first divisor polynomial g (x) divides xm' + 1, characterized in that the permuted sequence a * is given by

I> ,, 1. , A x'x '"where the matrix S * of s;, k is produced according to any one of claims 1 to 6. 18. Interleaver (101) suitable for providing, from a sequence a of <Desc / Clms Page number 36> Y-., -Y-., As * XIIll + A where the matrix S * of s *; is produced according to any one of claims 1 to 6.

polynomial a (x) = al Á .x 1111 th divisible by a first divisor polynomial g (x), and whose coefficients of increasing order are the binary data of the sequence a, a permuted sequence a * associated with a polynomial a * (x) whose coefficients of increasing order are the binary data of the sequence a *, said polynomial a * (x) being intended to be divided by a second divisor polynomial g * (x) compatible with the first divisor polynomial g (x), to form a sequence of binary data c, and a having a number of binary data equal to the product of any integer r by the integer m, m being a multiple of the smallest integer m 'such that the first divisor polynomial g (x) divides xm '+ 1, characterized in that the permuted sequence a * is given by

binary data representative of a physical quantity, associated with a 19. Coding device characterized in that it comprises an interleaver according to any one of claims 17 to 18. 20. Coding device according to claim 19, working on sequences of binary data u representative of information and taking into account

1-1 has a first divisor polynomial g (x = 9 + g, x + x ', a second divisor polynomial g * (x) compatible with g (x), a first multiplicative polynomial f1 (x) and a second multiplicative polynomial f2 (x), an integer r # 1, an integer m multiple of the smallest integer m 'such that the first polynomial g (x) divides xm' + 1, characterized in that it comprises: - means of constitution of a "first" sequence, called "sequence a" represented by a polynomial a (x) called "first polynomial" whose rm-t first coefficients of increasing order are the binary data to be coded and whose t last coefficients are chosen such that the polynomial g (x) divides the polynomial a (x) - means of constituting a second sequence called "sequence b" represented by a polynomial b (x) equal to the product of the first polynomial a ( x) by <Desc / Clms Page number 37> the first multiplicative polynomial f1 (x), the whole divided by the first divisor polynomial g (x), - permutation means, working on binary data of the first sequence a to form a so-called "permuted" sequence a * represented by a so-called "permuted" polynomial a * (x), whose coefficients of increasing order are the binary data of the permuted sequence a *, and which is divisible by the second divisor polynomial g * (x), - constitution means of a third sequence called "sequence c" represented by a polynomial c (x) equal to the product of the first polynomial a (x) by the second multiplicative polynomial f2 (x), the whole divided by the second divisor polynomial g * (x ). 21. Decoding device, characterized in that it implements at least one interleaver according to any one of claims 17 to 18 and / or a deinterleaver corresponding to this interleaver. 22. Turbo-decoding device characterized in that it implements at least one interleaver according to any one of claims 17 to 18 and / or a deinterleaver corresponding to this interleaver. 23. Device suitable for decoding sequences received after coding by a coding device according to any one of claims 19 to 20. 24. Device according to any one of claims 17 to 23, characterized in that it comprises a transmission means adapted to transmit, on the one hand, the sequence a, and, on the other hand, a subset of the. sequence data produced by the encoder. 25. A device for processing signals representative of speech, characterized in that it comprises a device according to any one of claims 17 to 24. 26. Data transmission device comprising a transmitter adapted to implement a packet transmission protocol, characterized in that it comprises a device according to any one of claims 17 to 25. 27. Data transmission device according to claim 26, characterized in that said protocol is the ATM, Asynchronous protocol. <Desc / Clms Page number 38> Transfer Mode. 28. Data transmission device according to claim 26, characterized in that said protocol is the IP protocol, Internet Protocol. 29. Data transmission device comprising a transmitter transmitting on a wireless channel, characterized in that it comprises a device according to any one of claims 17 to 28. 30. Network station, characterized in that it comprises a device according to any one of claims 17 to 29.