FR2801446A1 - Method for coding of a primary data sequence by generating first polynomial divider of cyclic codes whose generating polynomial is second polynomial divider - Google Patents

Abstract

A non trivial inter-columns permutation (506) transforms (507) a cyclic code of NO length for generating a first polynomial divider (g1(x)) of cyclic codes whose generating polynomial is the second polynomial divider (g2(x)), the inter-columns permutation. The NO columns of an image representing the sequence of origin (u) are permuted and each of which being a permutation of the symbols of a column of the image. Independent claims are included for: (a) a coding device (b) a method of decoding (c) a decoding device (d) a method of creating a look-up table (e) an apparatus for digital data processing (f) a telecommunication network (g) a mobile station used in a telecommunication network (h) a device for processing a signal representing password (i) a data transmission device

Description

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

More specifically, the present invention relates to a method and a turbo-coding and turbo-decoding device that does not require addition bits ("padding <I> bits" </ I>).

Conventionally, a turbocharger consists of three essential parts: two basic recursive convolutional coders and an interleaver.

The associated decoder consists of two elementary decoders with so-called soft inputs and outputs corresponding to the convolutional encoders, an interleaver and its inverse interleaver (also called "deinterleaver").

A description of the turbo codes can be found in the article "Near <I> Shannon </ I> limit error-correcting coding <I> and </ I> decoding: <I> turbo codes" </ I> corresponding to the presentation made by C. BERROU, A. GLAVIEUX and P. THITIMAJSHIMA at the ICC Conference in Geneva in May 1993.

Since the coders are systematic recursive, a problem that is often found is that of setting the encoders to zero.

Various ways of dealing with this problem can be found in the prior art, in particular 1. No resetting: the encoders are initialized in the zero state and allowed to evolve to any state without intervening. 2. Reset of the first encoder: the encoders are initialized in the null state and padding bits are added to impose a zero final state only on the first encoder.

3. "Frame Oriented Convolutional Turbo" (FOCTC): The first encoder is initialized and the final state of the second encoder is taken as the initial state of the second encoder. first encoder. When using a class of interleavers with certain properties, the final state of the second encoder is zero. Reference is made to this subject in the article by C. BERROU and M. JEZEQUEL entitled "Frame oriented convolutional turbo-codes", in Electronics Letters, Vol. 32, No. 15, July 18, 1996, pages 1362 to 1364, Stevenage, Herts, Great Britain.

4. Independent resets of the two coders: the encoders are initialized in the null state and padding bits are added independently to each of the sequences entering the coders. A general description of independent encoder resets is given in the report by D. DIVSALAR and F. POLLARA entitled "TDA progress report 42-123 <I> On the design </ i> <i> of turbo codes", < Published in November 1995 by Jet Propulsion Laboratory (JPL).

5. Intrinsic reset of the two encoders: the encoders are initialized in the null state and padding bits are added to the sequence that enters the first encoder. When using an interleaver guaranteeing the return to zero as explained in the patent document FR-A-2 773 287 and that the sequence comprising the padding bits is interleaved, the second coder automatically has a final state of zero.

For each of the solutions of the prior art mentioned above, there is a lattice termination adapted for each corresponding decoder. These decoders take into account the termination or not of the trellises, as well as, where appropriate, the fact that each of the two coders uses the same padding bits.

Solutions 1 and 2 have the drawback of generally offering poorer performance than solutions 3 to 5.

However, solutions 3 to 5 also have disadvantages. Consider solution 3, which uses frame-oriented convolutional turbocodes (FOCTCs).

The FOCTCs can be described in the following manner. A FOCTC-type turbocoder of output 1I3 can be considered as a convolutional recursive encoder implementing a divisor polynomial.

Let g (x) be the divisor polynomial of the encoder.

Let m be the degree of the polynomial g (x) and NO the smallest integer such that g (x) is a divisor of the polynomial x "+ 1. This number NO is called the" period "of g (x).

Let n be a multiple of NO: n = M.NO, where M is an integer.

The encoder produces a control sequence from a sequence of binary information symbols to be encoded u of length n and an interleaved sequence u * obtained by interleaving the sequence u.

The sequence of symbols u then has a polynomial representation u (x), of degree n -1, with binary coefficients. In the following, the notation u and u (x) are equivalent.

Thus, the encoder, from a sequence u represented by a polynomial u (x), produces a sequence v represented by a polynomial v (x) _ (u (x) + xM ".u * (x)). h (x) Ig (x), where h (x) and g (x) are two prime polynomials between them.

On the other hand, the sequence u (x) is interleaved into a sequence u * (x) by a permutation having a divisibility property described later.

These permutations are, in a representation where the binary data of the sequence u are written and read, line by line, in an array with NO columns and M lines, where NO is the smallest integer such that the divisor polynomial g (x) divides x "+1, the resultant of any number of so-called elementary permutations, each of which is any permutation of the symbols of a column of said array.

In the French patent application number 98 14086 depicting a family of interleavers compatible with FOCTC and simple to implement. An interleaver of this family is of the form "x to x" ", where e is a power of 2 modulo n and is congruent to 1 modulo N0, and this interleaver is defined as follows if u designates the input sequence and u * the permuted sequence, the interleaver switches each bit that is initially in position i in u, to a position (e.i modulo n) in u *.

Overall, the turbo encoder produces the sequences u and v, which are then transmitted on a transmission channel.

The divisibility property mentioned above, related to the permutation used, is that the sequence a (x) = u (x) + xM ".u * (x) is divisible by g (x). Thus, if the encoder is initialized to a null state, it returns to a null state after encoding the sequence a (x).

On the decoder side, a turbodecoder adapted to take into account the fact that - on the one hand, the initial state E ;, l of the first encoder and the final state of the second encoder Ef, 2 are null, and - on the other hand, the initial state E;, 2 of the second encoder is identical to the final state of the first encoder Ef ,,.

However, this solution 3 proposed by the prior art limits the choice of interleavers, which may reduce performance or unnecessarily complicate the realization of the interleaver.

As for solution 4, it performs worse than solution 5 when the size of the interleaver is small.

Finally, the solution 5 requires the addition bits ("padding <I> bits") </ I> to be determined before the second coder can start coding. Thus, the prior art does not solve the problem consisting, from a turbocode architecture similar to that implemented by the solution 3 mentioned above, to propose methods and devices for coding and decoding - offering a wide choice of interleavers, - allowing optimization of performance, and - allowing the use of interleavers of simple realization. The present invention aims to overcome the aforementioned drawbacks.

For this purpose, according to a first embodiment, the present invention proposes a method of coding at least one original binary data sequence, according to which - at least a first recursive convolutional coding operation is performed, consisting of coding the original sequence by a coding technique implementing a first divisor polynomial and not including any bit adding guaranteeing the divisibility by the first divisor polynomial; at least one interleaving operation is performed so as to obtain an interleaved sequence; and performing at least one second recursive convolutional coding operation, consisting of coding the interleaved sequence by an encoding technique implementing a second divisor polynomial and including no bit adding guaranteeing the divisibility by the second divisor polynomial, the second divisor polynomial being compatible with the first divisor polynomial; this coding method being remarkable in that - at least one interleaving operation consists of permuting the binary data of the original sequence by means of a specific permutation, this specific permutation being in a representation where the data bits of the original sequence are written and read, line by line, in an array with NO columns and M lines, where NO is the smallest integer such that the first divisor polynomial divides the polynomial x "+1 and M is a positive integer, the resultant of a non-trivial inter-column permutation, that is to say different from the identity permutation, which transforms the cyclic code of length NO whose generator polynomial is the first divisor polynomial into the cyclic code whose the generator polynomial is the second divisor polynomial, this inter-column permutation exchanging between them the NO columns of the array representing the original sequence, and a number that Each elementary permutations intra-column, each of these elementary permutations being any permutation of the symbols of a column of the aforementioned table.

Thus, the present invention makes it possible, for a given block size - to initialize the first coder to a zero state - to code the original sequence with this first coder into a sequence leading to a final state of the first coder. to interleave the original sequence in a permuted sequence, by a specific permutation preserving the divisibility by the divisor polynomial of the two coders, - to initialize the second encoder to an initial state depending both on the final state of the first encoder and inter-column permutation mentioned above, according to rules ensuring the return to zero of this encoder, and - to code with the second encoder the permuted sequence.

The divisibility property mentioned above allows the second encoder to have a null end state.

Overall, the turbo encoder produces the original sequence and sequences provided by the first and second encoders, which are transmitted later on a transmission channel.

According to a second embodiment, the present invention also proposes a method for coding at least one original binary data sequence, according to which at least one first recursive convolutional coding operation is performed, consisting of coding the sequence of origin by an encoding technique implementing a first divisor polynomial and not including any bit adding guaranteeing the divisibility by the first divisor polynomial; at least one interleaving operation is performed so as to obtain an interleaved sequence; and performing at least one second recursive convolutional coding operation, consisting in coding the interleaved sequence by an encoding technique implementing a second divisor polynomial and including no bit adding guaranteeing the divisibility by the second divisor polynomial, the second divisor polynomial being compatible with the first divisor polynomial; this coding method being remarkable in that - at least one interleaving operation consists of permuting the binary data of the original sequence by means of a specific permutation, this specific permutation being in a representation where the data bits of the original sequence are written and read, line by line, in an array with NO columns and M lines, where NO is the smallest integer such that the first divisor polynomial divides the polynomial x "+1 and M is a positive integer, the resultant of an inter-column permutation, which transforms the cyclic code of length NO whose generator polynomial is the first divisor polynomial into the cyclic code whose generator polynomial is the second divisor polynomial, this permutating inter-column permutation between them the NO columns of the table representing the original sequence, and any number of elementary permutations intra-column, each of these elementary rmutations being any permutation of the symbols of a column of the aforementioned table; this coding method is also remarkable in that the first coding operation includes a step of initialization to a null state and ends with any final state, and at least one second coding operation comprises an initialization step. to a null state and terminates at any final state depending on the final state of the first coding operation.

Thus, knowing the specific permutation and the final state of the first coding operation, it is possible to determine what will be the final state of the second coding operation.

This feature can simplify decoding, since initialization is the same in recursive convolutional encoding operations. In addition, the encoding of the interleaved sequence can begin before the encoding of the original sequence is completed. Moreover, in this second embodiment, the inter-column permutation can be either the identity or be non-trivial.

In this second embodiment, according to a particular characteristic, the coding method comprises at least one operation of one-to-one mapping between the possible final states of the first coding operation and the possible final states of at least one second operation of coding.

This feature is simple to implement and reduces the time required for coding.

In the second embodiment, according to a particular characteristic, the interleaving operation is of the "x to x" "type, where e is a power of 2 modulo M.NO.

This type of interleaving operation has the advantage of being simple to implement.

According to a particular characteristic of the first embodiment, the first coding operation comprises an initialization step at a zero initial state and ends at any final state, and at least a second coding operation comprises a step of initialization to an initial state dependent on the final state of the first coding operation and ending in a zero final state.

This feature has the advantage of simplifying the implementation of the corresponding decoding, while minimizing the additional complexity coding side.

According to one particular characteristic, the coding method of the invention comprises at least one univocal mapping operation between the possible final states of the first coding operation and the possible initial states of at least one second coding operation.

This feature is simple to implement and reduces the time required for coding. According to a particular characteristic of the first embodiment, the interleaving operation is of the "x to x" "type, where e is a power of 2 modulo M.NO and is not congruent to 1 modulo N0.

This type of interleaving operation has the advantage of being simple to implement.

In the first and second embodiments, according to a particular characteristic, the mapping operation depends on the inter-column permutation.

This limits the number of parameters or operations necessary for matching.

In the first and second embodiments, according to a particular characteristic, the dividing polynomials are identical.

This characteristic makes it possible to simplify the implementation of the coding.

For the same purpose as that indicated above, the present invention further proposes, according to a first embodiment, a device for coding at least one original binary data sequence, comprising: a first recursive convolutional coding module; to encode the original sequence by an encoding technique implementing a first divisor polynomial and not including any bit additions ensuring divisibility by this first divisor polynomial; an interleaving module for producing an interleaved sequence; and at least one second recursive convolutional coding module, for encoding the interleaved sequence by an encoding technique implementing a second divisor polynomial and including no adding of a bit guaranteeing the divisibility by this second divisor polynomial, the second divisor polynomial being compatible with the first divisor polynomial; this coding device being remarkable in that: the interleaving module comprises a module for permuting the binary data of the original sequence by means of a specific permutation, this specific permutation being in a representation where the data bits of the original sequence are written and read, line by line, in an array with NO columns and M lines, where NO is the smallest integer such that the first divisor polynomial divides the polynomial x "+1 and M is a positive integer, the resultant of a non-trivial inter-column permutation which transforms the cyclic code of length NO whose generator polynomial is the first divisor polynomial into the cyclic code whose generator polynomial is the second divisor polynomial, this inter-column permutation swapping between them the NO columns of the array representing the original sequence, and any number of elementary permutations within the column, ch acune elementary permutations being any permutation of the symbols of a column of the aforementioned table.

According to a second embodiment, the present invention proposes a device for coding at least one original binary data sequence, comprising - a first recursive convolutional coding module, for coding the original sequence by a coding technique implementing a first divisor polynomial and not including any bit adding guaranteeing the divisibility by this first divisor polynomial; an interleaving module for producing an interleaved sequence; and at least one second recursive convolutional coding module, for encoding the interleaved sequence by an encoding technique implementing a second divisor polynomial and including no adding of a bit guaranteeing the divisibility by this second divisor polynomial, the second divisor polynomial being compatible with the first divisor polynomial; this coding device being remarkable in that: the interleaving module comprises a module for permuting the binary data of the original sequence by means of a specific permutation, this specific permutation being in a representation where the data bits of the original sequence are written and read, line by line, in an array with NO columns and M lines, where NO is the smallest integer such that the first divisor polynomial divides the polynomial x "+1 and M is a positive integer, the resultant of an inter-column permutation which transforms the cyclic code of length NO whose generator polynomial is the first divisor polynomial into the cyclic code whose generator polynomial is the second divisor polynomial, this permutation inter-columns permutating between they are the NO columns of the table representing the original sequence, and any number of elementary permutations in the column, each of the elementary mutations being any permutation of the symbols of a column of the aforementioned table; this coding device is also remarkable in that: the first coding module is initialized to a null state and has any final state, and at least one second coding module is initialized to a null state and has any final state depending on the final state of the first coding module.

The advantages and the particular characteristics of these coding devices being the same as those of the coding methods according to the invention, they are not recalled here.

Still for the same purpose, the present invention further proposes a method for decoding at least one sequence of original symbols, which is remarkable in that the original symbol sequence is representative of a binary sequence encoded by using a coding method as above.

Such a decoding method has good performance and can benefit, in general, advantages mentioned above in connection with the coding.

In a first variant, the initial states of the coding operations are zero and the final state of the second coding operation depends on the final state of the first coding operation. In this first variant, according to a particular characteristic, the decoding method comprises at least one operation of one-to-one mapping between the possible final states of the first coding operation and the possible final states of at least one second coding operation.

In a second variant, the decoding method comprises at least one operation of one-to-one mapping between the possible final states of the first coding operation and the possible initial states of at least one second coding operation.

According to one particular characteristic, the decoding method implements decoding operations with soft inputs and soft outputs. This characteristic makes it possible to obtain good performances, with reduced complexity.

According to a particular characteristic, the following operations are performed iteratively: at least a first elementary operation for decoding a recursive convolutional code, consisting in decoding a first subsequence of said sequence of original symbols by a decoding technique implementing the first divisor polynomial is used and taking into account the initial state (E; j) and the final state (Ef 1) of the first coding operation; at least one interleaving operation of a sequence representative of the original sequence; at least one second elementary operation for decoding a recursive convolutional code, consisting in decoding a second subsequence of said original symbol sequence by a decoding technique implementing the second divider polynomial and taking into account the initial state (E; 2) and the final state (Ef 2) of the second coding operation; and at least one deinterleaving operation of a sequence representative of the interlaced origin sequence.

According to a particular characteristic, in an elementary decoding operation, the taking into account of an initial (respectively final) zero state of the corresponding coding operation is done by initialization of a node metric - with a probability of occurrence maximum for the initial (respectively final) state nil, - with a probability of occurrence nil for the initial (respectively final) non-zero states, - with an equiprobability of occurrence for all the final states (respectively initial) at 1 initialization of the first elementary decoding operation of the first iteration and with a probability of occurrence for all the final states (initial respectively) at the initialization of the following decoding operations which depends on the probabilities of occurrence of the final states or initials defined by the previous elementary decoding operation.

This takes into account the relationships between the final and initial states of the encoders, which improves performance.

The advantages of the particular features of the decoding method not expressly mentioned above are the same as those of the corresponding special features of the coding methods.

For the same purpose as above, the present invention furthermore proposes a device for decoding at least one sequence of original symbols, which is remarkable in that the sequence of original symbols is representative of a binary sequence coded at the first time. using a coding device as above.

The advantages of the decoding device being the same as those of the decoding method according to the invention, they are not recalled here. Moreover, there are for the decoding device particular characteristics similar to those of the decoding method, which have the same advantages.

In addition, according to one particular characteristic, the decoding device comprises a first calculation module, for assigning a value to each element of a node metric table used as input to a second elementary decoding module (which performs the second elementary decoding operation), as a function of each element of a node metric table derived from a first decoding elementary module (which performs the first elementary decoding operation).

In addition, according to one particular characteristic, the decoding device comprises a second calculation module, for assigning a value to each element of a node metric table used at the input of the first elementary decoding module, as a function of each element of the decoding module. a node metric table from the second basic decoding module.

Thanks to the two particular characteristics above, good decoding performance is obtained, thanks to a good match between decoder and encoder.

For the same purpose as above, the present invention also proposes a method of creating a correspondence table between all the possible final states of a first recursive convolutional coder of a coding device such as that of the first embodiment mentioned. above, the first recursive convolutional encoder implementing a first divisor polynomial, and all the possible initial states of a second recursive convolutional encoder of the encoding device, the second recursive convolutional encoder implementing a second divisor polynomial compatible with the first divisor polynomial, this method of creation being remarkable in that, for each possible final state of the first coder, an initial state of the second encoder of all possible initial states is chosen such that the final state of the second coder is zero . This simplifies the production of coding and decoding devices. In a particular embodiment, a first construction operation is performed, consisting in constructing a transition table from a current state of the first encoder to the next state as a function of the bit supplied to the input of the first encoder; a second construction operation is carried out, consisting of constructing a table making it possible to determine, from the transitions table obtained previously, a first sequence which, starting from a current state of the first coder, leads to a final state of zero. ; an addition operation is performed, consisting in adding to the first sequence as many null bits as necessary to obtain a second sequence having NO bits, NO being the smallest integer such that the divisor polynomial of the first encoder divides the polynomial x " +1; an interleaving operation is performed, consisting of interleaving the second sequence with an inter-column permutation, so as to obtain a third sequence, the inter-column permutation being non-trivial and having the effect of transforming the cyclic code of length NO and having as polynomial generator the first dividing polynomial in an equivalent cyclic code having as generator polynomial the second polynomial divider, this permutation inter-columns acting by permutation on the NO columns of an array representing the second sequence, in a representation where the binary data of the second sequence are written and read, line by line, in a table with NO columns and M rows, M being a positive integer; and performing a third construction operation, consisting of constructing a table for determining the final state of a recursive convolutional coder initialized to a null state, having the divisor polynomial as the second divisor polynomial and used to obtain the third sequence; to obtain a fourth table establishing the correspondence between the final state of the first coder and the initial state of the second coder for the inter-column permutation used.

This particular embodiment makes it possible either to compute "on the fly" the initial state of the second coder, without a correspondence table, or to create a correspondence table between the initial states of the second coder and the final states of the first coder. when the above method is applied to all possible end states of the first encoder. According to a particular characteristic, in the above coding method, the mapping operation between all the possible final states of the first coding operation and all possible initial states of at least one second coding operation involves covers a correspondence table created by a creation method - a correspondence table between all the possible final states of the first encoder and all possible initial states of the second encoder, as above.

According to one particular characteristic, the decoding method above, when it comprises at least one mapping operation of all the possible final states of the first coding operation and all possible initial states of at least one second coding operation, uses a correspondence table created by a method of creating a correspondence table between all the possible final states of the first coder and all possible initial states of the second coder, as above.

For the same purpose as above, the present invention also proposes a method of creating a correspondence table between all the possible final states of a first recursive convolutional coder of a coding device such as that of the second embodiment mentioned above. above, the first recursive convolutional encoder covering a first divisor polynomial, and all possible end states of a second recursive convolutional encoder of the encoding device, the second recursive convolutional encoder covering a second divisor polynomial compatible with the first divisor polynomial, this method of creation being remarkable in that, for each possible final state of the first encoder, a final state of the second encoder is determined among all the possible final states when the initial state of the second encoder is zero.

This feature can simplify decoding, since initialization is the same in recursive convolutional encoding operations. In addition, the encoding of the interleaved sequence can begin before the encoding of the original sequence is completed.

According to one particular characteristic, the above decoding method, when it comprises at least one mapping operation of all the possible final states of the first coding operation and all possible final states of at least one second coding operation, uses a correspondence table created by a method of creating a correspondence table between all the possible final states of the first coder and all the possible final states of the second coder, as above.

The present invention also provides a digital signal processing apparatus, comprising means adapted to implement a coding method and / or a decoding method as above.

The present invention also relates to a digital signal processing apparatus, comprising a coding device and / or a decoding device as above.

The present invention also relates to a telecommunications network, comprising means adapted to implement a coding method and / or a decoding method as above.

The present invention also relates to a telecommunications network, comprising a coding device and / or a decoding device as above.

The present invention also relates to a mobile station in a telecommunications network, comprising means adapted to implement a coding method and / or a decoding method as above.

The present invention also relates to a mobile station in a telecommunications network, comprising a coding device and / or a decoding device as above.

The present invention also relates to a representative speech signal processing device, comprising a coding device and / or a decoding device as above.

The present invention also relates to a data transmission device comprising a transmitter adapted to implement a packet transmission protocol, comprising a coding device and / or a decoding device and / or a device for processing representative speech signals. as above.

According to a particular characteristic of the data transmission device, the packet transmission protocol is of the ATM (asynchronous transfer mode) type.

In a variant, the packet transmission protocol is of the IP (transmission protocol used over the Internet, in English "Internet Protocol") type .The invention also aims at - a means of storing information that can be read by a computer or a microprocessor that retains instructions of a computer program, allowing the implementation of a coding method as above, and - a removable information storage medium, partially or completely, readable by a computer or a microprocessor retaining instructions of a computer program, allowing the implementation of a coding method as above.

The invention also aims at - a computer-readable information storage means or a microprocessor retaining instructions of a computer program, allowing the implementation of a decoding method as above, and - a means partially or fully removable information storage device readable by a computer or a microprocessor retaining instructions of a computer program, allowing the implementation of a decoding method as above.

The invention also relates to a computer program comprising instruction sequences for implementing a method of coding and / or decoding and / or creation of a correspondence table as above.

The particular characteristics and the advantages of the different digital signal processing apparatus, the different telecommunications networks, the various mobile stations, the representative speech signal processing device, the data transmission device, the information storage means and the computer program being the same as those of the methods and devices of coding and decoding according to the invention, they are not recalled here.

Other aspects and advantages of the invention will appear on reading the following detailed description of particular embodiments, given by way of non-limiting examples. The description refers to the accompanying drawings, in which: - Figure 1 shows schematically an electronic device comprising a coding device according to the present invention, in a particular embodiment; - Figure 2 shows schematically, in block diagram form, a coding device corresponding to a parallel convolutional turbocode, according to the present invention, in a particular embodiment; FIG. 3 diagrammatically represents an electronic device comprising a decoding device according to the present invention, in a particular embodiment; - Figure 4 shows schematically, in block diagram form, a decoding device corresponding to a parallel convolutional turbocode, according to the present invention, in a particular embodiment; FIG. 5 is a flowchart showing schematically the operation of a coding device such as that included in the electronic device of FIG. 1, in a particular embodiment; FIG. 6 is a flowchart showing schematically decoding operations implemented by a decoding device such as that included in the electronic device of FIG. 3, according to the present invention, in a particular embodiment; FIG. 7 is a flowchart schematically showing a turbodecoding operation included in the flowchart of FIG. 6, in a particular embodiment of the present invention; and FIG. 8 schematically represents a coding device corresponding to a convolutional turbocode including several inputs, according to an alternative embodiment of the present invention. In general, a turbocoder of the type of those appearing in the invention, having the output 1I3, can be considered as a pair of convolutional recursive coders using divisor polynomials. The first encoder produces a control sequence from a sequence of symbols to be encoded u and the second encoder produces a control sequence from an interleaved sequence u * obtained by interleaving the sequence u.

Let gi (x) be the divisor polynomial of the first encoder.

Let m be the degree of the polynomial g, (x) and NO the smallest integer such that gi (x) is a divisor of the polynomial x "+1 This number NO is called the" period "of gi (x).

Let 92 (x) be the divisor polynomial of the second encoder.

est la factorisation complète de gi(x) dans un corps d'extension du corps à deux éléments, alors la factorisation complète de 92(x) est

où cp est un automorphisme (noté exponentiellement) dudit corps d'extension. Dans la suite, un tel polynôme 92(x) sera dit compatible avec gi(x). En particulier, un polynôme est toujours compatible avec lui-même. On remarquera que deux polynômes compatibles ont le même degré et la même période. gi (x) and 92 (x) have the following property:

is the complete factorization of gi (x) in an extension body of the two-element body, then the complete factorization of 92 (x) is

where cp is an automorphism (exponentially noted) of the extension body. In the following, such a polynomial 92 (x) will be said to be compatible with gi (x). In particular, a polynomial is always compatible with itself. It will be noted that two compatible polynomials have the same degree and the same period.

Consider for example the factorization gi (x) = (x - #) (xu 2) (x-a4) of g, (x) = x3 + x + 1 where a is a primitive root seventh of the unit and belongs to the body containing eight elements. Consider the six automorphisms <B> (Pi </ B>: a -> ai of this eight-element body.) We verify that <B> (pi, </ B> cp2 and (p4 produce 92 (x) = 9 , (x) while cp3, cps and (p5 produce 92 (x) = x3 + x2 +1 which factorizes as 92 (X) = (X- (X 3) (x-as) (x- (X5) .

In the following, we assume that gi (x) = 92 (x). By convention, gi (x) and 92 (x) will be denoted g (x).

Let n be a multiple of NO: n = M.NO, where M is an integer.

The first encoder produces a control sequence from a sequence of binary information symbols to be encoded u of length n. The sequence of symbols u has a polynomial representation u (x), of degree n -1, with binary coefficients.

As an illustration, we consider in the following a divisor polynomial g (x) equal to 1 + x2 + x3. His period, N0, is worth 7.

We consider a coding sequence of 147 bits (n = 147) and polynomials h <B> l </ B> (x) and h2 (x) both equal to 1 + x + x3.

Under these conditions, an interleaver preserving the divisibility by g (x) must have a size multiple of 7; if we write the data line by line in a 7-column table, we can swap the data inside each column in any way and swap the columns together according to certain conditions preserving the divisibility by g (x), before reading the permuted data line by line.

By numbering the columns in increasing order from 0 to 6, we denote (bo, bl, ..., bk) the permutation that moves the column of rank bo to rank b ,, the column of rank b, to rank b2 , ... and the column of rank bk to rank bo.

We denote (cc, ci, ..., ck) (do, d1, ..., dk @) the compound of two permutations (co, cl, ..., ck) and (do, di, ... , dk @).

The following table T lists the 167 non-trivial inter-column permutations that preserve the divisibility by g (x).

(1 <SEP> 2 <SEP> 4) <SEP> (3 <SEP> 6 <SEP> 5) <SEP> (1 <SEP> 4 <SEP> 2) <SEP> (3 <SEP> 5 <SEP > 6)
<tb> (0123456) <SEP> (026) (143) <SEP> (046) (325)
<tb> (02461 <B> 35) </ b><SEP> (045) (1 <SEP> 62) <SEP> (01 <SEP> 5) <SEP> (364)
<tb> (0362514) <SEP> (064) (235) <SEP> (054) (126)
<tb> (04 <SEP> 1 <SEP><B> 5263) <SEP> (0 <SEP> 1 <SEP> 3) (254) <SEP><B> (023) (1 <SEP> 65) </ B>
<tb> (0531642) <SEP> (032) (156) <SEP> (062) (134)
<tb> (0654321) <SEP> (051) <SEP> (346) <SEP> (03 <SEP> 1) (245)
<tb> (1 <SEP><B> 5) (23) <SEP> (1 <SEP> 3 <SEP> 6) <SEP> (2 <SEP> 4 <SEP> 5) <SEP > (1 <SEP> 4 <SEP> 3) <SEP> (2 <SEP> 5 <SEP> 6)
<tb><B> (056) (1 </ B><SEP> 34) <SEP> (0 <SEP> 3 <SEP> 5 <SEP> 1 <SEP> 4 <SEP> 2 <SEP> 6) <SEP> (046) (2 <SEP> 1 <SEP> 5)
<tb><B> (031 </ B><SEP> 2465) <SEP> (0416325) <SEP> (05) (2364) <SEP>,
<tb> (02 <SEP><B> 1 </ B> 4) (36) <SEP> (0 <SEP> 6 <SEP> 4) <SEP> (3 <SEP> 1 <SEP> 5) <SEP> (0 <SEP> 1 <SEP><B> 32654) </ B>

(0 <SEP> 4 <SEP> 5 <SEP> 3) <SEP> (2 <SEP> 6) <SEP> (0 <SEP> 5 <SEP> 4 <SEP> 3) <SEP> (1 <SEP > 2) <SEP><B> (03) (1 </ B><SEP> 6)
<tb> (0 <SEP><B> 164352) <SEP> (0 <SEP> 2) <SEP> (5 <SEP> 6) <SEP> (0 <SEP> 6 <SEP> 3 <SEP> 4 <SEP> 5 <SEP> 1 <SEP> 2)
<tb> (0 <SEP> 6 <SEP> 1) (2 <SEP> 5 <SEP> 4) <SEP> (0 <SEP> 1) (2 <SEP> 3 <SEP> 4 <SEP> 6) <SEP> (0 <SEP> 2 <SEP> 4 <SEP> 1) <SEP> (3 <SEP> 5)
<tb> (2 <SEP> 3) <SEP> (4 <SEP> 6) <SEP> (1 <SEP> 3 <SEP> 4) <SEP> (2 <SEP> 6 <SEP> 5) <SEP > (1 <SEP> 6 <SEP> 2) <SEP> (3 <SEP> 5 <SEP> 4)
<tb> (0 <SEP> 1 <SEP><B> 36) (45) <SEP> (031 </ B><SEP> 6) (24) <SEP> (0 <SEP> 6) <SEP> (2 <SEP> 5)
<tb> (0 <SEP> 3 <SEP> 5) <SEP> (1 <SEP> 2 <SEP> 6) <SEP> (0 <SEP> 6 <SEP> 3 <SEP> 2 <SEP> 1 <MS> 4 <SEP> 5) <SEP> (0 <SEP> 1 <SEP> 5) (234)
<tb> (0251634) <SEP> (04) (53) <SEP> (0561324)
<tb> (0624153) <SEP> (0125643) <SEP><B> (03) (1 </ B><SEP> 465)
<tb> (0 <SEP> 5 <SEP> 2) (1 <SEP> 4 <SEP> 3) <SEP> (02) (1 <SEP> 546) <SEP> (04 <SEP> 1 <SEP><B> 2) (36) </ B>
<tb> (0421) (56) <SEP> (051) (362) <SEP> (0264531)
<tb> (1 <SEP> 5) (46) <SEP> (1 <SEP> 2 <SEP> 6) <SEP> (3 <SEP> 4 <SEP> 5) <SEP> (1 <SEP> 6 <SEP> 3) <SEP> (2 <SEP> 5 <SEP> 4)
<tb> (0541236) <SEP> (0243516) <SEP><B> (06) (1 <SEP> 532) </ B>
<tb> (0 <SEP> 2 <SEP> 6 <SEP> 5) <SEP> (1 <SEP> 3) <SEP> (0 <SEP> 6 <SEP> 2 <SEP> 5) <SEP> ( 1 <SEP> 4) <SEP> (0 <SEP> 5) <SEP> (3 <SEP> 4)
<tb> (034) (1 <SEP><B> 62) </ B><SEP> (04) (1 <SEP><B> 523) <SEP> (01 </ B><SEP> 24) (56)
<tb> (0 <SEP> 6 <SEP> 3) <SEP> (2 <SEP> 4 <SEP> 5) <SEP> (056421 <SEP> 3) <SEP> (0 <SEP> 2 <SEP> 3) <SEP> (1 <SEP> 4 <SEP> 6)
<tb> (0 <SEP> 1 <SEP> 4 <SEP> 2) <SEP> (3 <SEP> 5) <SEP> (0 <SEP> 3 <SEP> 2) <SEP> (4 <SEP> 6 <SEP> 5) <SEP> (0451 <SEP><B> 362) </ B>
<tb> (0432561) <SEP> (01) (36) <SEP> (0352641)
<tb> (2 <SEP> 4) <SEP> (3 <SEP> 6) <SEP> (1 <SEP> 4) (56) <SEP> (1 <SEP><B> 2) (35) < / B>
<tb> (0145326) <SEP> (046) (123) <SEP> (0256) (34)
<tb> (0 <SEP> 4 <SEP> 3 <SEP> 5) <SEP> (1 <SEP> 6) <SEP> (02 <SEP> 1 <SEP><B> 3645) <SEP> (01 <SEP> 5) (624)
<tb> (064) (1 <SEP><B> 25) <SEP> (0 <SEP> 3 <SEP> 5 <SEP> 4) <SEP> (2 <SEP> 6) <SEP > (0 <SEP> 5 <SEP> 2 <SEP> 3 <SEP> 6 <SEP> 1 <SEP> 4)
<tb> (023) (154) <SEP> (0163) (25) <SEP> (0426513)
<tb> (0562) (13) <SEP><B> (061 </ B><SEP> 5342) <SEP> (032) (164)
<tb> (0346521) <SEP> (051) (324) <SEP> (0631) (45)
<tb> (1 <SEP> 5) <SEP> (2 <SEP> 4 <SEP> 3 <SEP> 6) <SEP> (1 <SEP> 4 <SEP> 5 <SEP> 6) <SEP> ( 2 <SEP> 3) <SEP> (1 <SEP><B> 3) (25) </ B>
<tb> (0526) (14) <SEP> (046) (135) <SEP> (0342156)
<tb> (0423 <SEP><B> 165) </ B><SEP> (03641 <SEP> 25) <SEP> (05) <SEP> (2463)
<tb> (064) (1 <SEP><B> 32) <SEP> (02631 </ B><SEP> 54) <SEP><B> (014) (365) </ B>

(0 <SEP> 3) <SEP> (4 <SEP> 5) <SEP> (0 <SEP> 5 <SEP> 3) <SEP> (1 <SEP> 6 <SEP> 2) <SEP> (043 ) (1 <SEP><B> 26) </ B>
<tb> (0 <SEP> 1 <SEP><B> 2) (356) <SEP> (0 <SEP> 6 <SEP> 5 <SEP> 2) (3 <SEP> 4) <SEP> (02) (1 <SEP> 645)
<tb> (0253461) <SEP> (01) (24) <SEP> (0623541)
<tb> (2 <SEP> 6) <SEP> (3 <SEP> 4) <SEP> (1 <SEP> 6 <SEP> 5 <SEP> 4) <SEP> (2 <SEP> 3) <SEP > (1 <SEP> 3 <SEP> 5 <SEP> 2) <SEP> (4 <SEP> 6)
<tb><B> (01 </ B><SEP> 6) (245) <SEP><B> (06) (1 </ B><SEP> 3) <SEP> (0 <SEP> 3 <SEP> 6) <SEP> (2 <SEP> 5 <SEP> 4)
<tb> (0614235) <SEP> (0345) (12) <SEP> (015) (263)
<tb> (04) (1 <SEP><B> 325) <SEP> (0 <SEP> 2 <SEP> 4) <SEP> (3 <SEP> 5 <SEP> 6) <SEP > (0 <SEP> 5 <SEP> 3 <SEP> 4) (1 <SEP> 6)
<tb><B> (03) (1 </ B><SEP> 564) <SEP> (0146253) <SEP><B> (0651 </ B><SEP> 243)
<tb> (0546312) <SEP> (0436152) <SEP> (02) (14)
<tb> (021) (365) <SEP> (051) (264) <SEP> (0456231)
<tb> (1 <SEP> 5) <SEP> (2 <SEP> 6 <SEP> 3 <SEP> 4) <SEP> (1 <SEP> 6) <SEP> (4 <SEP> 5) <SEP > (1 <SEP> 2 <SEP> 5 <SEP> 3) <SEP> (4 <SEP> 6)
<tb> (0532416) <SEP><B> (06) (1 <SEP> 235) </ B><SEP> (0215436)
<tb><B> (065) (1 </ B><SEP> 43) <SEP><B> (025) (1 </ B><SEP> 34) <SEP> (0 <SEP> 5) <SEP> (2 <SEP> 6)
<tb> (04) (12) <SEP><B> (031 </ B><SEP> 5624) <SEP> (0165234)
<tb> (0 <SEP> 2 <SEP> 3) <SEP> (4 <SEP> 5 <SEP> 6) <SEP> (0 <SEP> 5 <SEP> 2 <SEP> 1 <SEP> 4 <SEP> 6 <SEP> 3) <SEP><B> (061 </ B><SEP> 3) (24)
<tb> (0135462) <SEP> (042) (365) <SEP> (032) (145)
<tb> (0 <SEP> 3 <SEP> 6 <SEP> 1) <SEP> (2 <SEP> 5) <SEP> (0 <SEP> 1) <SEP> (2 <SEP> 6 <SEP> 4 <SEP> 3) <SEP> (0 <SEP> 4 <SEP> 1) <SEP> (3 <SEP> 5 <SEP> 6)
<tb> Table <SEP> T An interleaver having a simple implementation is for example an interleaver "x to x32" defined as follows: if u designates the input sequence and u * the permuted sequence, this interleaver switches each bit in position i in u to a position (32.i modulo 147) in u *.

This interleaver can be obtained by the combination of: (i) inter-column permutation (1 4 2) (3 5 6), which is given in the table of inter-column permutations given above and (ii) permutations within columns. Thus, this interleaver preserves the divisibility by g, while maintaining a simple implementation. In general, we can use interleavers of the form "x to xe", where e is a power of 2 modulo n and is not congruent to 1 modulo N0, which allows to exclude the case of the permutation between -columns equal to the identity.

These interleavers are defined as follows if u designates the input sequence and u * the permuted sequence, the interleaver switches each bit that is initially in position i in u, to a position (e.i modulo n) in u *.

We now describe how we can determine the initial state E;, 2 of the second systematic recursive convolutional coder from the final state Ef, j of the first systematic recursive convolutional coder and the inter-column permutation.

Consider a parallel convolutional turbocoder with a feedback polynomial g (x) of period N0.

Let u (x) be the sequence to be coded of length n.

Consider a permutation preserving the divisibility, for example of the type described in the patent document FR-A-2 773 287 cited in the introduction.

This permutation corresponds to a row-column interleaver with NO columns where data is written and read line by line. This permutation is composed of an inter-column permutation II and intra-column permutations.

Let u * (x) be the result of this permutation applied to u (x). The encoding of u (x) could be done as follows - step 1: first code u with the first systematic recursive convolutional coder, consisting essentially of a shift register and initialized to a zero state. The first encoder is then in a final state Ef, j.

step 2: with this same coder, a sequence p ,, defined as the residue modulo g (x) of u is determined. For this, it is enough to reinject the feedback bit at the input of the encoder (for more details on this point, one can refer to the report of D. DIVSALAR and F. POLLARA quoted in the introduction). This encoder is then in the null state. Then we complete the sequence pi by zeros to obtain a formal degree equal to N0. Then, a sequence p'l is determined, resulting from the inter-column permutation iI applied to pi.

The sequence p '<B> <U>, </ U> </ B> is then coded with the second systematic recursive convolutional coder, initialized to a zero state. The second encoder is then in an initial state E ;, 2.

step 3: the interlaced sequence u * is coded with the second coder in this initial state E;, 2. Thanks to the properties of the interleaver and as a result of the operations performed in step 2, the second coder is in a final state of zero.

However, it is not very useful to transmit the addition bits and the coding bits from step 2: the sequences pi and p 'carry no information.

Their only utility is to change the state of the encoders between the encoding of u and u *.

Moreover, the set of possible initial states E;, 2 of the second coder is linked one-to-one with the set of possible final states Ef, i of the first encoder as a function of the inter-column interleaver used.

This is why, in accordance with the invention, step 2 is replaced by a simpler step 2 ', described hereinafter: step 2': the second encoder is initialized to a state E;, 2 as a function of E , l and inter-column interleaver used.

The relations between E;, 2, Ef ,, and the inter-column interleaver can be predefined and stored in memory in a correspondence table. This correspondence table can in particular be obtained by applying step 2 to all states Ef, i possible.

Similarly, on the decoder side, the portion of the trellis corresponding to step 1 and the part of the trellis corresponding to step 3 can be directly connected: each possible node at the end of the first trellis is then simply connected to one and a single node at the beginning of the second lattice. The notion of FOCTC is thus extended to all turbo-codes using interleavers preserving the divisibility of u (x) + x ".u * (x) by g (x) and not only to those in which the cross-column permutation is identity.

By way of example, the following method can be used to determine the relations between E;, 2, Ef, j and the inter-column interleaver.

For a given current state of a binary input convolutional encoder, the next state depends only on the bit entering this encoder.

A transition table from a current state to a next state can be constructed as a function of the encoder input bit (see Table 1 below), corresponding to a recursive convolutional encoder having a feedback polynomial g (x) = 1 + x2 + x3.

State <SEP> current <SEP> State <SEP> next <SEP> State <SEP> next
<tb> with <SEP> 0 <SEP> in <SEP> entry <SEP> with <SEP> 1 <SEP> in <SEP> entry
<tb> 000 <SEP> 000 <SEP> 100
<tb> 001 <SEP> 100 <SEP> 000
<tb> 010 <SEP> 101 <SEP> 001
<tb> 011 <SEP> 001 <SEP> 101
<tb> 100 <SEP> 010 <SEP> 110
<tb> 101 <SEP> 110 <SEP> 010
<tb> 110 <SEP> 111 <SEP> 011
<tb> 111 <SEP> 011 <SEP> 111
<tb> Table <SEP> 1 From this transition table, it is possible to determine a sequence p, of three bits which, from a current state of the encoder Ef ,,, leads to a final state of the encoder which is no. We give below the table (table 2) of such sequences pi.

Ef, <SEP> l <SEP> p,
<tb> 000 <SEP> 0

001 <SEP> 1
<tb> 010 <SEP> 1 + x
<tb> 011 <SEP> x
<tb> 100 <SEP> x + x2
<tb> 101 <SEP> 1 <SEP> + x + x2
<tb> 110 <SEP> 1 + x2
<tb> 111 <SEP> x2
<tb> Table <SEP> 2 From this table, a sequence p'l obtained by adding four null bits to the pi sequence and then interleaving with the inter-column permutation used is determined.

Consider, by way of example, an inter-column permutation II = (1 4 2) (3 5 6) acting on 7-bit sequences.

From table 2, we determine the interleaved sequence p'l, resulting from the column permutation applied to the sequence p extended to 7 bits and equaling [p, () pp, 2 0 0 0 0] (with p1 (x ) = plo + p, l.x + pl2.x2).

Thus, p ', (x) = plo + px4 + p12.x = Plo + Pl2.x + Pll.x4.

We can then determine the final state E; 2 of a convolutional convolutional encoder of feedback polynomial g (x), initialized to a null state and used to code the sequence p'l, by constructing the following table 3

p, <SEP>p'1 = Plo + Pi2.x + Pll.x4 <SEP> Ei, 2
<tb> (notation
<tb> polynomial)
<tb> 0 <SEP> 0 <SEP> 000
<tb> 1 <SEP> 1 <SEP> 001
<tb> 1 + x <SEP> 1 + x4 <SEP> 100
<tb> x <SEP> x4 <SEP> 101
<tb> x + x2 <SEP> x + x4 <SEP> 110
<tb><B> 1 </ B><SEP> + x + x2 <SEP> 1 + x + x4 <SEP> 111

1 <SEP> + x` <SEP><B> 1 + x </ B><SEP> 010
<tb> x2 <SEP> x <SEP> 011
<tb> Table <SEP> 3 One can thus, from tables 1 to 3 above, form a table 4 as below, summarizing the correspondence between E;, 2 and Ef, j for the inter-column permutation. defined, for the purposes of the example given here, by (1 4 2) (3 5 6) with g (x) = 1 + x2 + x3

E <SEP> Ei, 2
<tb> 000 <SEP> 000
<tb> 001 <SEP> 001
<tb> 010 <SEP> 100
<tb> 011 <SEP> 101
<tb> 100 <SEP> 110
<tb> 101 <SEP> 111
<tb> 110 <SEP> 010
<tb> 111 <SEP> 011
<tb> Table <SEP><B> 4 </ B> Table 4 is a lookup table that gives E;, 2 in a one-to-one manner in terms of Ef, j and can both be used - on the turbocharger, to correctly initialize the second recursive convolutional encoder according to the final state of the first encoder and - on the turbo decoder side, to define the decoding trellis.

Moreover, the turbodecoding is an iterative operation well known to those skilled in the art. For further details, reference may be made to the article by J. HAGENAUER, E. OFFER and L. PAPKE entitled "Iterative decoding <I> of </ I> binary <I> block and </ I> convolutional <I> codes ", </ I> in IEEE Transactions on Information Theory, March 1996, - in the article by J. HAGENAUER, P. ROBERTSON and L. PAPKE entitled" lterative (turbo) decoding <I> of </ I> systematic convolutional codes with <I> the </ I> MAP <I> and </ I> SOVA algorithms ", in Informationstechnische Gesellschaft (ITG) Fachbericht, pages 21 to 29, October 1994 and - in the article of C BERROU, S. EVANO and G. BATTAIL entitled "Turbo-block-codes", published with the proceedings of the "turbo coding" seminar organized by the Lund Institute of Technology (Sweden) (Department of Applied Electronics) in August 1996.

Nevertheless, care will be taken to properly construct the trellises which are generally used with reference to Table 4 given above.

We will now describe a particular embodiment of the present invention, using FIGS. 1 to 8.

<B> Figure 1 </ B> 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 ROM 105 <B>; </ B> and - 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 preferentially adapted to provide signal sequences representative of speech, service messages or multimedia data, in the form of binary data sequences, and that the radio transmitter 106 is adapted to implement a packet transmission protocol on a 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 104 and 105, both a low capacitance memory zone (a few binary data) and a high capacity memory zone (for storing a memory). 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. The random access memory 104 comprises in particular - a "data <I> source" register, </ I> in which are kept, in the order of their arrival on the bus 102, the binary data coming from the information source 110 in the form of a sequence u, - a register "nb <I> data", </ I> which keeps an integer corresponding to the number of binary data n in the register "data <I> source", </ I a register <I> "data permuted", </ I> in which are kept, in the order of their arrival on the bus 102, the binary data exchanged, as described further with the aid of FIG. 5 , in the form of a sequence u *, and - a register <I> "data to be issued", </ I> in which are preserved the sequences to be transmitted.

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 register <I> program ", </ I> - the sequence g, in a register" g ", the degree m of g (x), in a register" m ", the sequence h1, in a register" h1 ", - the sequence h2, in a register "h2", - the value of N0, in a register "NO", - the value of n, in a register "n", - the array defining the interleaver, in a register "interleaver" and a correspondence table giving E; 2 as a function of Ef, l, in a register "table E; 2 = f (Efl)", this correspondence table being constructed beforehand, for example according to the method previously described using tables 1 to 4.

The central processing unit 100 is adapted to implement the flowchart illustrated in FIG. 5.

FIG. 2 shows that a coding device corresponding to a parallel convolutional turbocode, in accordance with the present invention, comprises in particular - a symbol input 201 to be coded, where the information source 110 provides a sequence of binary symbols to transmit, or "to code", u, - a first encoder 202, which provides, from the sequence u, a sequence vi of symbols representative of the sequence u, - an interleaver 203, which provides, from the sequence u, an interleaved sequence u *, whose symbols are the symbols of the sequence u, but in a different order, - a second encoder 204, which provides, from the interleaved sequence u *, a sequence v_2 of representative symbols of the sequence u *, and - a calculation operator 205, which determines the initial state E;, 2 of the second encoder 204 as a function of the final state Ef, l of the first encoder 202.

The three sequences u, v, and v2 are transmitted to be, then, decoded.

In the remainder of the description, preference is given to "x to x32" type interleavers of size 147, although the present invention is not limited to this type of interleaver, but relates, more generally, to all types of interleavers. interleavers preserving divisibility by g (x), with non-trivial inter-column permutation <B> Fi </ B>.

FIG. 3 schematically illustrates the constitution of a network station or computer decoding station, in the form of a block diagram.

This station comprises a keyboard 311, a screen 309, an external information recipient 310, a radio receiver 306, jointly connected to an input / output port 303 of a processing card 301.

The processing card 301 comprises, interconnected by an address and data bus 302 - a central processing unit 300; a RAM RAM 304; a ROM memory 305; and - the input / output port 303.

Each of the elements illustrated in Figure 3 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 recipient 310 is, for example, an interface device, a display, a modulator, an external memory or another information processing system (not shown), and is preferentially adapted to receive signal sequences representative of speech, service messages or multimedia data, in the form of binary data sequences, and - the radio receiver 306 is adapted to implement a packet transmission protocol on a channel not wired, and to receive these packets on such a channel.

It is further observed that the word "register" used in the description designates, in each of the memories 304 and 305, both a memory zone of low capacity (a few binary data) and a memory zone of large capacity (allowing store an entire program). The RAM 304 stores data, variables and intermediate processing results, in memory registers carrying, in the description, the same names as the data whose values they retain. The RAM 304 includes in particular - a register <I> "data received", </ I> in which is conserved, in the order of arrival of the binary data on the bus 302 from the transmission channel, a soft estimate of these binary data, equivalent to a measurement of reliability, in the form of a sequence, - a register "inf extrinsic", in which are kept, at a given moment, the extrinsic information corresponding to the sequence u, - a register < I> "estimated data", </ I> in which is kept, at a given instant, an estimated sequence - outputted by the decoding device of the invention, as described later with the help of Figure 4 a register "nb iteration", which keeps an integer corresponding to an iteration counter performed by the decoding device concerning a received sequence u, as described below with the help of FIG. 4, and - a register "nb <i> data", </ i> which keep an integer corresponding to the number of binary data in the <I> "data received" register. </ i>

The read-only memory 305 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 300, in a register <I>. ", </ I> - the array defining the interleaver and its inverse interleaver, in an" interleaver "register, - the sequence g, in a register" g ", - the degree m of g (x), in a register "m", - the sequence hl, in a register <I> "hl", </ I> - the sequence h2, in a register "h2", - the value of n, in a register "n", - the value of <I> N0, </ I> in a register <I> "NO", </ I> - the predetermined maximum number of iterations to be performed during the turbodecoding operation 603 of a received u sequence, described below with the aid of FIGS. 6 and 7, in a register "nb iteration max", and - a correspondence table giving Ei, 2 as a function of Ef ,, in a register "table E; 2 = f (Efl ) ", this table being identical to that which is present in the coder, in the ROM 105.

The central processing unit 300 is adapted to implement the flowchart illustrated in FIG. 6.

FIG. 4 shows that a decoding device comprises in particular three inputs 401, 402 and 403 of sequences representative of u, v, and v2 which, for convenience, are also denoted u, v, and v2, the sequence received consisting of these three sequences, being denoted r; a first soft input / output decoder 404 (in English "soft <I> input </ I> output ') corresponding to the encoder 202 (FIG. 2) The first decoder 404 receives as input - the sequences u and vi, - a extrinsic information sequence w4, and - a node metric table Ef, lin described below The first decoder 404 outputs - a posterior estimation sequence wi, - an estimated sequence on an output 410, and a node metric table Ef ,, out.

The decoding device illustrated in FIG. 4 furthermore comprises an interleaver 405 (denoted "Interleaver 1T in FIG. 4), based on the same permutation as that defined by the interleaver 203 used in the coding device: the interleaver 405 receives as input the sequences u and w, and interleaves them respectively into sequences u * and w2; - an operator 412, which assigns a value to each element of the node metric table Ei, 2i, intended for a second decoder 406 as a function of each element of the node metric table Ef, the output of the first decoder 404 and of the correspondence table giving E;, 2 as a function of Ef, the operation carried out amounts to linking each n # ud initial (corresponding to a state E;, 2) of the lattice used by the second decoder at each final node (corresponding to a state Ef, j) of the lattice used by the first decoder in a one-to-one manner according to the correspondence table e E; 2 = f (Ef 1) present in the ROM 305; the second soft input / output decoder 406 corresponding to the second encoder 204.

This second decoder 406 receives as input - the sequences u * and v2, - the extrinsic information sequence w2, and - a metric table of n # ud E;, 2; n described below. The second decoder 406 outputs - an extrinsic information sequence w3, - an estimated sequence û *, and - a metric table of n # ud E;

The decoding device illustrated in FIG. 4 further comprises - a deinterleaver 408 (denoted "interleaver 17-li 'in FIG. 4), opposite to the interleaver 405, receiving as input the sequence φ * and outputting an estimated sequence on an output 409 (this estimate being improved with respect to that provided, a half-iteration previously, on the output 410); a deinterleaver 407 (also referred to as "interleaver I7-" in FIG. interleaver 405, receiving as input the extrinsic information sequence w3 and outputting the extrinsic information sequence W4 - an operator 413, which assigns a value to each element of the metric table of n # ud Ef, for the first decoder 404, as a function of each element of the metric table of n # ud E;, 2o, t from the second decoder 406 and the correspondence table giving E;, 2 as a function of Ef, j the operation performed returns to rel ier each initial node (corresponding to a state E;, 2) of the lattice used by the second decoder to each final node (corresponding to a state Ef, f) of the lattice used by the first decoder in a one-to-one manner according to from the correspondence table E;, 2 = f (Ef ,,) present in the ROM 305; and the output 409, on which the decoding device provides the estimated sequence, at the output of the deinterleaver 408. An estimated sequence is taken into account only after a predetermined number of iterations (see FIG. "Near <I> Shannon </ I> <i> error - </ I> correcting coding <I> and </ I> decoding <I>: </ I> turbocodes" cited above).

In the preferred embodiment described here, one can use a BJCR type algorithm (named after its authors BAHL, COCKE, JELINEK and RAVIV) for each of the decoders 404 and 406. This algorithm is generally used in connection with the turbocodes. A description of the BJCR algorithm can be found in the article by LR BAHL, J. COCKE, F. JELINEK and J. RAVIV entitled <I> "Optimal </ I> decoding <I> of </ I> linear <I > codes for </ I> minimizing symbol errorrate, in IEEE Transactions on Information Theory, March 1974.

The naeuds metrics of the first decoder 404 can be initialized as follows - with a maximum probability of occurrence for the initial null state, - with a zero probability of occurrence for non-zero initial states, - with equal probability for all end states at the first iteration and - with a probability for each end state defined by the node metric table Ef, l; n for subsequent iterations.

After each elementary decoding operation, the node metrics corresponding to the final state are updated in the node metric table E f, by identification with the metrics of corresponding nodes provided by the first decoder 404.

The node metrics of the second decoder 406 can be initialized as follows - with a maximum probability of occurrence for the final null state, - with a zero occurrence probability for non-zero end states and - with a probability for each state initial defined by the metric table of n # ud E;, 2;,.

After each elementary decoding operation; the node metrics corresponding to the final state are updated in the metric table of n # ud E; 2out by identification to the metrics of corresponding nodes provided by the second decoder 406.

In general, whatever the algorithm used, the various parameters necessary for the proper functioning of this algorithm will be initialized within each of the decoders, taking into account the initial and final states of each of the coders as well as the properties that bind.

In FIG. 5, which represents the operation of a coding device such as that included in the electronic device illustrated in FIG. 1, it is observed that after an initialization operation 500, during which the registers of the random access memory 104 are initialized (nb <I> data = "0"), </ I> during an operation 501, the central unit 100 waits to receive, then receives a binary data item to be transmitted, places it in random access memory 104 in the <I> "source data" </ I> register and increments the "nb <I> data" </ I> counter by one unit. Then, during a test 502, the central unit 100 determines whether the whole number stored in the "nb <I> data" </ I> register is equal to n or not (value conserved in the read-only memory 105).

When the result of the test 502 is negative, the operation 501 is repeated. When the result of the test 502 is positive, during an operation 508, the first coder 202 (see FIG. 2), initialized to a zero state, performs the division according to the increasing powers (in English <I> "long < / I> <I> division ") </ I> by g (x) of the polynomial u (x) associated with the binary data sequence u and - a multiplication by h1 (x). The sequence u and the result vi of this operation are stored in the <I> "data-to-send" </ I> register of the random access memory 104.

Then during an operation 511, by reading the correspondence table giving E; 2 as a function of Ef ,,, stored in the register "table E; 2 = f (Efl)" of the ROM 105, we determine the initial state E;, 2 of the second encoder 204, from the final state Ef, j of the first encoder 202 at the end of the operation 508.

In parallel with the operations 508 and 511, during an operation 506, the binary data of the sequence u are successively read in the <I> "received data" register, </ I> in the order described by the table "interlea The data of the sequence u *, which successively results from this reading, are stored in the <I> "data permuted" </ I> register of the random access memory 104.

Then, during an operation 507, the second encoder 204, initialized in the state E; 2, performs the division according to the increasing powers per g (x) of the sequence u * and the product of the result of this division by h2 (x).

The result v2 of this operation is stored in the "data-to-<I> transmit" </ I> register of the random access memory 104.

During an operation 509, the sequences u, vi and v2 are transmitted using, for this purpose, the transmitter 106 (see FIG. 1). Then, the registers of the memory 104 are initialized again. In particular, the counter nb <I> data </ I> is reset to "0" and the operation 501 is reiterated.

In FIG. 6, which represents the operation of a decoding device such as that included in the electronic device illustrated in FIG. 3, it is observed that after an initialization operation 600, during which the RAM registers 304 are initialized (nb <I> data = "0"), </ I> during an operation 601, the central processing unit 300 waits to receive, then receives a data item in a soft form corresponding to a reliability measure of a data transmitted by the transmitter 106 and received by the receiver 306, places it in RAM 304, in the <I> "data </ I> received" register and increments the counter "nb <I> data" </ I > a unit. Then, during a test 602, the central unit 300 determines whether the whole number stored in the "nb <I> data" </ I> register is equal to or not equal to 3.n (where n is a conserved value in ROM 305), where 3.n is the total number of binary data transmitted by the transmitter 106.

When the result of the test 602 is negative, the operation 601 is repeated.

When the result of the test 602 is positive, during a turbodecoding operation 603, detailed below, the decoding device gives an estimate of the transmitted sequence u.

Then, during an operation 604, the CPU 300 provides this estimate to the information recipient 310.

Then, the registers of the memory 304 are again initialized. In particular, the counter nb <I> data </ I> is reset to "0" and operation 601 is reiterated.

In FIG. 7, which details the turbodecoding operation 603, it is observed that during an initialization operation 700, the registers of the random access memory 304 are initialized: the counter nb <I> data </ I> and the extrinsic information w2 and w4 are reset (it is assumed here that the entropy of the source is zero). Moreover, the node metric table Ef, j; r ,, intended for the first decoder 404 (see FIG. 4) is initialized so that all the nodes are equiprobable. In addition, the interleaver 405 interleaves the input sequence u and provides a sequence u *, which is stored in the <I> received data </ I> register of the RAM 304.

Then, during an operation 702, the register number iteraiion is incremented by one unit.

Then, during an operation 703, the first decoder 404 (corresponding to the first elementary encoder 202) implements an algorithm of the type with soft inputs and soft decisions (SISO, in English "Soft Input Soft Output"), well known those skilled in the art, such as BJCR, mentioned above, or SOVA ("Soft <I> Output </ I> Viterbi Algorithm"), as follows taking into account an initial state of the null encoder and metrics of nodes for the final state equal to the corresponding values of the metric table of ## EQU1 ## the first decoder 404 considers as soft inputs an estimate of the received sequences u, vf, and w4 (extrinsic information on u), then supply w, (extrinsic information on u), an estimate of the sequence u and a table of metrics of n # ud for the final state updated Ef, lo, t.

For more details on the decoding algorithms used in turbocodes, reference may be made to the article by LR BAHL, J. COCKE, F. JELINEK and J. RAVIV cited above, which describes an algorithm called "BJCR". generally used in connection with turbocodes, or - in the article by J. HAGENAUER and P. HOEHER entitled <I> "A </ I> Viterbi algorithm with either decision outputs <I> and </ I> its <I > applications ", </ I> published with the proceedings of the IEEE GLOBECOM conference, pages 1680-1686, in November 1989.

During an operation 705, the interleaver 405 interleaves the sequence wi to produce w2, extrinsic information on u *.

Meanwhile, during an operation 704, the operator 412 updates a node metric table E ;, 2 ;, for the initial state of the second decoder, according to the node metric table Ef, fo t for the final state of the first decoder 404, according to the correspondence table giving E; 2 as a function of Ef, f, stored in the register "table E; 2 = f (Efl)" in the ROM 305 : for each possible state i, E;, 2;, (i) = Ef ,, out (f (i)).

Then, during an operation 706, the second decoder 406 (corresponding to the second elementary coder 204) implements an algorithm of the type with soft inputs and soft decisions, as follows: taking into account a final state of the second null coder and node metrics for the initial state equal to the corresponding values of the metric table of n # ud, 2; ", the second decoder 406 considers as soft inputs an estimate of the received sequences u *, v2, and w2 (extrinsic information on u) then provides w3 (extrinsic information on u *), an estimate û * of sequence u * and a table of metrics of n # ud for the initial state of second encoder update E;, 2out During an operation 708, the deinterleaver 407 (inverse interleaver 405) deinterleaves the information sequence w3 to produce w4, extrinsic information on u.

Meanwhile, during an operation 707, the operator 413 updates a node metric table Ef ,,; n for the final state of the first decoder, according to the node metric table E; , t for the initial state of the second decoder 406, according to the correspondence table giving Ef ,, as a function of Ei, 2 (obtained simply by inverse reading of the function giving Ei, 2 from Ef ,,, which is a bijective function), stored in the register "table Ei2 = f (Ef,)" in the read only memory 305: for each possible state i, Ef, 1in (f (i)) = Ei, 2out (i).

The extrinsic information produced in steps 703 and 706 is stored in the "inf extranesque" register of RAM 304.

Then, during a test 709, the central unit 300 determines whether the whole number stored in the register "nb iterafion" is equal or not to a predetermined maximum number of iterations to be performed, kept in the register "nb iteration max "of the ROM 305.

When the result of the test 709 is negative, the operation 702 is repeated.

When the result of the test 709 is positive, during an operation 710, the deinterleaver 408 (identical to the deinterleaver 407) deinterleaves the sequence û *, to provide a deinterleaved sequence to the CPU 300, which then transforms the soft decision. in hard decision, in the form of a sequence û, estimated from u.

In the preferred embodiment, the case has been exposed where the initial state of the second encoder was unspecified and its final state, zero.

In a variant, the invention can be applied in the same way when the initial state of the second coder is zero and its final state is arbitrary. In this case, we use an interleaver preserving the divisibility by the divisor polynomial of the coders with an inter-column permutation which is either the identity or one of the 167 permutations defined in the table T given above. In general, we can use interleavers of the form "x to xe", where e is a power of 2 modulo n.

The final states of the two coders are then linked to each other in the same way as were the final state of the first coder and the initial state of the second coder. Only the roles of the initial and final states of the second coder or decoder are exchanged.

Thus, a correspondence table Ef, 2 = f (Ef ,,) is constructed such that if the encoders are initialized in the zero state, if the first encoder has a final state Ef, j, the second encoder will have a final state Ef, 2; Ef, 2 depends only on Ef, j and the inter-column permutation used, in a one-to-one way. In the case where this permutation is the identity, Ef, j and Ef, 2 are equal.

The advantage of this variant is that one does not need to know the final state of the first coder to perform the coding by the second coder: this provides a simplification and this allows simultaneous coding by the two coders. On the decoder side, apart from the role change, there is essentially no difference between this variant and the preferred embodiment.

In particular, as an alternative to the decoding device illustrated in FIG. 4 and described above, the operator 412 assigns a value to each element of the metric table of n # ud Ef, 2; n (instead of E; 2in) for the second decoder 406, as a function of each element of the metric table of ## EQU1 ## issuing from the first decoder 404; the second decoder 406 receives as input a metric table of n # ud Ef, 2; n (instead of E;, 2; n); the second decoder 406 outputs a metric table of n # ud Ef, 2o ,, t (instead of E;, 2o, t); the operator 413 assigns a value to each element of the metric table of n # ud Ef, l;, intended for the first decoder 404, as a function of each element of the metric table of n # ud Ef, 2out (at place of E;, 2out) issuing from the second decoder 406 and from the correspondence table giving Ef, 2 (instead of E; 2) as a function of Efj; - the node metrics of the second decoder 406 can be initialized as follows - with a maximum probability of occurrence for the initial (instead of final) zero state, - with a probability of zero occurrence for the initial states (instead non-null endpoints and - with a probability for each end state (instead of initial) defined by the node metric table Ef, 2 ;, (instead of E;, 2; ,,); and - after each elementary decoding operation, the node metrics corresponding to the final state are updated in the node metric table Ef, 2oUt (instead of E; 2out) by identification to the corresponding node metrics provided by the second decoder 406.

In another variant, more general, the invention is not limited to turbo encoders composed of two coders or turbochargers with one input: it can be applied to turbochargers composed of several elementary coders or multi-input turbochargers, such as those described in the report by D. DIVSALAR and F. POLLARA quoted in the introduction.

In this case, it will be ensured that the interleavers used preserve the divisibility by the generator polynomial (s) used and that the elementary coders are correctly initialized, in accordance with what is done in the various cases described above. It will then be possible to establish the relationships that bind the add bits and use these relationships in the decoding device in a manner similar to what has been discussed above.

Thus, FIG. 8 describes a coding device comprising a multi-input turbocoder μ1, u2,..., Pk_1, uk in accordance with the invention.

Interleavers <B> 11, </ B> 12, ..., Ik_1, Ik, denoted by reference numerals 801 to 804, retain the divisibility by the feedback polynomial g (x) used in coders 805 and 806 .

An operator 807 determines the initial state E 1, 2 of the second coder, using a correspondence table, as a function of the final state Ef, 1 of the first coder.

 The corresponding decoding device can be easily deduced from the description of the coding device, on the basis of the description of the decoding device given above in the case where it considered a single input and a single interleaver.

Claims (43)

<U> CLAIMS </ U> A method of encoding at least one original binary data sequence (u), wherein - at least a first recursive convolutional encoding step (508) is performed, encoding said original sequence (u) by an encoding technique implementing a first divisor polynomial (gi (x) and not including any bit adding guaranteeing divisibility by said first divisor polynomial (gi (x; - performing at least one interleaving operation (506) , so as to obtain an interleaved sequence (u *); and - performing at least a second recursive convolutional coding operation (507), of encoding said interleaved sequence (u *) by a coding technique implementing a second a divisor polynomial (92 (x)) and not including any bit additions ensuring divisibility by said second divisor polynomial (92 (x)), said second divisor polynomial (92 (x)) being compatible with said first divisor polynomial (g); i (x), said coding method being characterized in that - at least one interleaving operation (506) consists of permuting the binary data of the original sequence (u) by means of a specific permutation, said specific permutation being, in a representation where the binary data of the original sequence (u) are written and read, line by line, in an array with NO columns and M lines, where NO is the smallest integer such that the first polynomial divider divides the polynomial x "+1 and M is a positive integer, the resultant of a non-trivial inter-column permutation (II) which transforms the cyclic code of length NO whose generator polynomial is said first divisor polynomial (gi ( x in the cyclic code whose generator polynomial is said second divisor polynomial (92 (x)), said inter-column permutation (II) permutating between them the NO columns of the array representing the original sequence (u), and of u n any number of intra-column elementary permutations, each of said elementary permutations being any permutation of the symbols of a column of said array. A method of encoding at least one original binary data sequence (u), wherein - at least a first recursive convolutional encoding step (508) is performed, encoding said original sequence (u) by a coding technique implementing a first divisor polynomial (gi (x)) and not including any bit additions guaranteeing divisibility by said first divisor polynomial (gi (x)); performing at least one interleaving operation (506) so as to obtain an interleaved sequence (u *); and performing at least a second recursive convolutional coding operation (507), of encoding said interleaved sequence (u *) by a coding technique implementing a second polynomial divider (92 (x)) and not including any adding a bit ensuring divisibility by said second divisor polynomial (92 (x)), said second divisor polynomial (92 (x)) being compatible with said first divisor polynomial (gi (x)); said coding method being characterized in that - at least one interleaving operation (506) is to swap the binary data of the original sequence (u) by means of a specific permutation, said specific permutation being, in a representation where the binary data of the original sequence (u) are written and read, line by line, in an array with NO columns and M lines, where NO is the smallest integer such that the first divisor polynomial divides the polynomial x "+1 and M is a positive integer, the resultant of an inter-column permutation (II) which transforms the cyclic code of length NO whose generator polynomial is said first divisor polynomial (gi (x)) into the code cyclic whose generator polynomial is said second divisor polynomial (92 (x)), said inter-column permutation (II) permutating between them the NO columns of the array representing the original sequence (u), and any number of permu Intra-columnary elementary units, each of said elementary permutations being any permutation of the symbols of a column of said array; said coding method being further characterized in that - the first coding operation (508) comprises an initialization step at a zero state (E; j) and ends at any final state (Ef, f), and at least one second coding operation (507) comprises an initialization step at a zero state (E; 2) and ends at a final state (Ef, 2) depending on the final state (Ef, j ) of the first coding operation (508). 3. Encoding method according to claim 2, characterized in that it comprises at least one operation of one-to-one correspondence between the possible final states (Ef, f) of the first coding operation (508) and the possible final states. (Ef, 2) at least a second coding operation (507). 4. Encoding method according to claim 2 or 3, characterized in that the interleaving operation (506) is of the type "x to x" ", where e is a power of 2 modulo M.NO. 5. Encoding method according to claim 1, characterized in that the first coding operation (508) comprises an initialization step at a zero initial state (E; j) and ends at a final state (Ef, j) any, and - at least one second coding operation (507) comprises an initial state initialization step (E;, 2) depending on the final state (Ef, j) of the first coding operation ( 508) and ends at a final state (Ef, 2) zero. 6. Encoding method according to claim 1 or 5, characterized in that it comprises at least one univocal mapping operation between the possible final states (Ef ,,) of the first coding operation (508) and the possible initial states (E;, 2) of at least one second coding operation (507). 7. Coding method according to any one of claims 1, 5 and 6, characterized in that the interleaving operation (506) is of the type "x to xe", where e is a power of 2 modulo M. NO and is not congruent to 1 modulo N0. 8. coding method according to any one of claims 3, 4, 6 and 7, characterized in that the mapping operation depends on the interchanging permutation (II). 9. Coding method according to any one of the preceding claims, characterized in that the divisor polynomials (gi (x), 92 (x)) are identical. Apparatus for encoding at least one original binary data sequence (u), comprising - first recursive convolutional encoding means (202), for encoding said original sequence (u) by a coding technique implementing a first divisor polynomial (gi (x)) and including no bit adding guaranteeing divisibility by said first divisor polynomial (gi (x)); interleaving means (203) for producing an interleaved sequence (u *); and at least second recursive convolutional coding means (204) for encoding said interleaved sequence (u *) by an encoding technique implementing a second divisor polynomial (92 (x)) and not including any bit additions guaranteeing divisibility by said second divisor polynomial (92 (x)), said second divisor polynomial (92 (x)) being compatible with said first divisor polynomial (gi (x)); said coding device being characterized in that - said interleaving means (203) comprises means for swapping the binary data of the original sequence (u) by means of a specific permutation, said specific permutation being, in a representation where the binary data of the original sequence (u) are written and read, line by line, in an array with NO columns and M lines, where NO is the smallest integer such as the first divisor polynomial (gi (x)) divides the polynomial x "+1 and M is a positive integer, the resultant of a non-trivial inter-column permutation (II) having the effect of transforming the cyclic code of length NO and having the generating polynomial said first polynomial divisor (gi (x)) in an equivalent cyclic code having for said generator polynomial said second divisor polynomial (92 (x)), said inter-column permutation (II) acting by permutation on the NO columns of the array the original sequence (u), and any number of intra-column elementary permutations, each of said elementary permutations being any permutation of the symbols of a column of said array. Apparatus for encoding at least one original binary data sequence (u), comprising - first recursive convolutional encoding means (202), for encoding said original sequence (u) by an encoding technique implementing a first divisor polynomial (gi (x)) and including no bit adding guaranteeing divisibility by said first divisor polynomial (gi (x)); interleaving means (203) for producing an interleaved sequence (u *); and at least second recursive convolutional coding means (204) for encoding said interleaved sequence (u *) by an encoding technique implementing a second divisor polynomial (92 (x)) and not including any bit additions guaranteeing divisibility by said second divisor polynomial (92 (x)), said second divisor polynomial (92 (x)) being compatible with said first divisor polynomial (gi (x)); said coding device being characterized in that - said interleaving means (203) comprises means for swapping the binary data of the original sequence (u) by means of a specific permutation, said specific permutation being, in a representation where the binary data of the original sequence (u) are written and read, line by line, in an array with NO columns and M lines, where NO is the smallest integer such as the first divisor polynomial (gi (x)) divides the polynomial x "+1 and M is a positive integer, the resultant of an inter-column permutation (II) having the effect of transforming the cyclic code of length NO and having as generator polynomial said first divisor polynomial (gi (x)) to an equivalent cyclic code having for said generator polynomial said second divisor polynomial (92 (x)), said inter-column permutation (II) acting by permutation on the NO columns of the array representing the quence of origin (u), and any number of intra-column elementary permutations, each of said elementary permutations being any permutation of the symbols of a column of said array; said coding device being further characterized in that - the first coding means (202) are initialized to a state (E; j) of zero and have any final state (Ef, j), and - at least second means encoding means (204) are initialized to a zero state (E; 2) and have any final state (Ef, 2) dependent on the final state (Ef, j) of the first encoding means (202). 12. Encoding device according to claim 11, characterized in that it comprises means of one-to-one correspondence between the possible final states (Ef, l) of the first coding means (202) and the possible final states (Ef, 2) at least second coding means (204). 13. Encoding device according to claim 11 or 12, characterized in that the interleaving means (203) are of the type "x to x", where e is a power of 2 modulo M.NO. 14. Encoding device according to claim 10, characterized in that the first coding means (202) are initialized to a zero initial state (E; j) and have a final state (Ef, j) of any kind, and at least second coding means (204) are initialized to an initial state (E; 2) dependent on the final state (Ef ,,) of the first coding means (202) and have a final state (Ef 2 ) no. Coding device according to claim 10 or 14, characterized in that it comprises means of one-to-one correspondence between the possible final states (Ef, I) of the first coding means (202) and the possible initial states ( E; 2) of at least second coding means (204). 16. Encoding device according to any one of claims 10, 14 and 15, characterized in that the interleaving means (203) are of the type "x to x" ", where e is a power of 2 modulo M. NO and is not congruent to 1 modulo N0. 17. Encoding device according to any one of claims 12, 13, 15 and 16, characterized in that the mapping means use the interchanging permutation (rI). 18. Encoding device according to any one of claims 10 to 17, characterized in that the divisor polynomials (gi (x), 92 (x)) are identical. 19. A method of decoding at least one sequence of origin symbols, characterized in that the sequence of original symbols is representative of a binary sequence (u) coded using a coding method according to any of claims 1 to 9. 20. Decoding method according to claim 19, characterized in that it implements decoding operations (703, 706) with soft inputs and soft outputs. 21. Decoding method according to claim 19 or 20, characterized in that it performs iteratively the following operations - at least a first elementary operation of decoding a recursive convolutional code (703) of decoding a first sub-sequence of said sequence of original symbols by a decoding technique implementing the first divisor polynomial (gi (x)) and taking into account the initial state (E; j) and the final state (Ef, j) the first coding operation (508); at least one interleaving operation (705) of a sequence representative of the original sequence; at least one second elementary decoding operation of a recursive convolutional code (706), consisting in decoding a second subsequence of said original symbol sequence by a decoding technique implementing the second divider polynomial (92 ( x)) and taking into account the initial state (E; 2) and the final state (Ef 2) of the second coding operation (507); and at least one deinterleaving operation (708) of a sequence representative of the interlaced origin sequence. 22. Decoding method according to claim 21, characterized in that, in an elementary decoding operation (703, 706), taking into account an initial (respectively final) zero state of the corresponding coding operation (508). , 507) is done by initialization of a metric of n # ud - with a maximum probability of occurrence for the initial state (respectively final) null, - with a probability of occurrence null for the initial states (respectively final) non-zero, - with an equiprobability of occurrence for all the final states (respectively initial) at the initialization of the first elementary decoding operation of the first iteration and - with a probability of occurrence for all the final states (respectively initial ) at the initialization of the following decoding operations which depends on the probabilities of occurrence of the final or initial states defined by the preceding elementary decoding operation ente. 23. Device for decoding at least one sequence of original symbols, characterized in that the sequence of original symbols is representative of a binary sequence (u) coded using a coding device according to any of claims 10 to 18. 24. The decoding device according to claim 23, characterized in that it implements decoding operations (703, 706) with soft inputs and soft outputs. 25. Decoding device according to claim 23, characterized in that it comprises - at least first elementary means for decoding a recursive convolutional code (404), for decoding a first subsequence of said sequence of symbols. of origin by a decoding technique implementing the first polynomial divisor (g, (x)) and taking into account the initial state (E ,, j) and the final state (Ef, j) of the first coding (202); at least one interleaving means (405) of a sequence representative of the original sequence; at least second elementary means for decoding a recursive convolutional code (406), for decoding a second subsequence of said original symbol sequence by a decoding technique implementing the second divisor polynomial (92 (x )) and taking into account the initial state (E; 2) and the final state (Ef 2) of the second coding means (204); and at least one deinterleaving means (407, 408) of a sequence representative of the interlaced origin sequence, said elementary decoding, interleaving and deinterleaving means (404, 405, 406, 407, 408) operating iteratively. 26. A decoding device according to claim 25, characterized in that, in the elementary decoding means (404, 406), taking into account an initial (respectively final) zero state of the corresponding coding means (202, 204). ) is done by initialization of a node metric - with a maximum probability of occurrence for the initial (final) state zero, - with a probability of occurrence null for the initial (final) non-zero states, - with an equiprobability of occurrence for all final states (respectively initial) at the initialization of the first elementary decoding means of the first iteration and - with a probability of occurrence for all the final states (initial respectively) at initialization subsequent decoding means which depends on the probabilities of occurrence of the final and initial states defined by the previous elementary decoding means. 27. Decoding device according to claim 25 or 26, characterized in that it comprises first calculation means (412) for assigning a value to each element of a node metric table (Ei, 2i,) used. at the input of the second elementary decoding means (406), as a function of each element of a node metric table (Ef, iout) issuing from the first elementary decoding means (404). 28. Decoding device according to claim 25, 26 or 27, characterized in that it comprises second calculation means (413), for assigning a value to each element of a node metric table (Ef, lin) used at the input of the first elementary decoding means (404), as a function of each element of a node metric table (Ei, 2out) issuing from the second elementary decoding means (406). 29. A method of creating a correspondence table between all the possible final states (Ef, j) of a first recursive convolutional encoder (202) of a coding device according to any one of claims 10 and 14 to 18. , said first recursive convolutional encoder (202) implementing a first divisor polynomial (g, (x)), and all possible initial states (Ei, 2) of a second recursive convolutional encoder (204) of said encoding device, said second recursive convolutional encoder (204) implementing a second divisor polynomial (92 (x)) compatible with said first divisor polynomial (gi (x)), said authoring method being characterized in that, for each possible end state ( Ef, i) of the first encoder (202), selecting an initial state (Ei, 2) of the second encoder (204) from among all possible initial states (Ei, 2) so that the final state (Ef, 2 ) of the second encoder (204) is zero. 30. Creation method according to claim 29, characterized in that a first construction operation is carried out, consisting of constructing a table of transitions (table 1) from a current state of the first coder (202) to the next state. depending on the bit input of the first encoder (202); a second construction operation is performed, consisting in constructing a table (table 2) making it possible to determine, from the transition table (table 1) obtained previously, a first sequence (pl) which, starting from a state current (Ef, 1) of the first encoder (202), leads to a zero final state; an addition operation is performed, consisting of adding to said first sequence (pi) as many null bits as necessary to obtain a second sequence having NO bits, NO being the smallest integer such that the divisor polynomial (gi (x) ) of the first encoder (202) divides the polynomial x "+1; - an interleaving operation is performed, consisting of interleaving said second sequence with an inter-column permutation (II), so as to obtain a third sequence (p ') ,), said inter-column permutation (II) being non-trivial and having the effect of transforming the cyclic code of length NO and having for generating polynomial said first divisor polynomial (gi (x)) into an equivalent cyclic code having for generator polynomial said second polynomial divider (92 (x)), said inter-column permutation (II) acting by permutation on the NO columns of an array representing said second sequence, in a representation where the given The binaries of the second sequence are written and read, line by line, in an array with NO columns and M lines, where M is a positive integer; and a third construction operation is carried out, consisting in constructing a table (table 3) for determining the final state (E; 2) of a recursive convolutional coder initialized to a zero state, having as divisor polynomial the second polynomial divisor (92 (x)) and used to obtain the third sequence (p'1); to obtain a fourth table (table 4) establishing the correspondence between the final state (Ef, l) of the first coder (202) and the initial state (E;, 2) of the second coder (204) for said permutation inter-columns (II). 31. A method of creating a correspondence table between all the possible final states (Ef, l) of a first recursive convolutional encoder (202) of a coding device according to any one of claims 11 to 13 and 17. , 18, said first recursive convolutional encoder (202) implementing a first divisor polynomial (gi (x)), and all possible end states (Ef, 2) of a second recursive convolutional encoder (204) of said encoder said second recursive convolutional coder (204) implementing a second divisor polynomial (92 (x)) compatible with said first divisor polynomial (gi (x)), said authoring method being characterized in that for each possible end state (Ef, j) of the first encoder (202), determining a final state (Ef, 2) of the second encoder (204) among all possible end states (Ef, 2) when the initial state (E;, 2) the second encoder (204) is zero. 32. Coding method according to any one of claims 6 to 9, characterized in that the mapping operation implements a correspondence table created by a creation method according to claim 29 or 30. 33. Decoding method according to any one of claims 19 to 22, characterized in that it uses a correspondence table created by a creation method according to claim 29, 30 or 31. 34. Apparatus for processing digital signals, characterized in that it comprises means adapted to implement a coding method according to any one of claims 1 to 9 and 32 and / or a decoding method according to one of any of claims 19 to 22 and 33. 35. Apparatus for processing digital signals, characterized in that it comprises a coding device according to any one of claims 10 to 18 and / or a decoding device according to any one of claims 23 to 28. 36. Telecommunication network, characterized in that it comprises means adapted to implement a coding method according to any one of claims 1 to 9 and 32 and / or a decoding method according to any one of the claims. 19 to 22 and 33. 37. Telecommunication network, characterized in that it comprises a coding device according to any one of claims 10 to 18 and / or a decoding device according to any one of claims 23 to 28. 38. Mobile station in a telecommunications network, characterized in that it comprises means adapted to implement a coding method according to any one of claims 1 to 9 and 32 and / or a decoding method according to the any of claims 19 to 22 and 33. 39. Mobile station in a telecommunications network, characterized in that it comprises a coding device according to any one of claims 10 to 18 and / or a decoding device according to any one of claims 23 to 28. 40. Apparatus for processing representative speech signals, characterized in that it comprises a coding device according to any one of claims 10 to 18 and / or a decoding device according to any one of claims 23 to 28. 41. 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 10 to 18 and / or a decoding device according to any one of claims 23 to 28 and / or a speech representative signal processing device according to claim 40. 42. Device for transmitting data according to claim 41, characterized in that said protocol is of ATM type. 43. Device for transmitting data according to claim 41, characterized in that said protocol is of IP type.