Interleaver for turbo codes as a function of the puncturing pattern

1. A method comprising:

encoding an input digital message bearing K information symbols using a turbo-encoder forming a turbocode, the turbo-encoder comprising an interleaver and first and second encoders for encoding according to at least one elementary code and delivering said information symbols and redundancy symbols,

wherein, with a puncturing of the symbols delivered by the turbo-encoder being done according to at least one periodic puncturing pattern of a length N, defining the puncturing period, said interleaver distributes the information symbols of said input message into Q layers of the interleaved input message in complying with an interleaving function defined from said at least one puncturing pattern, according to the relationship:

π( i )= Pi+S ( i mod Q )mod K=Pi +( T l +A l Q )mod K

with:

i=0, . . . , K−1 being the position of an information symbol in said interleaved input message, in the interleaved order and π(i) the position of said information symbol in said input message, in the natural order;

P an integer value co-prime with the length K of said input message, called an interleaver period;

S(i mod Q)=S(l)=T l +A l Q are the parameters of adjustment of the interleaving function, with l=0, . . . , Q−1 the layer number;

Q a degree of disorder inserted into the interleaver, corresponding to the number of layers, such that Q=qN, with q≥1 being an integer and Q being a divider of K;

T l a value of inter-layer adjustment defined from said at least one puncturing pattern; and

A l a value of intra-layer adjustment.

2. The method according to claim 1 , wherein, said puncturing implementing a puncturing of the information symbols delivered by said turbo-encoder, the value of inter-layer adjustment T l makes the punctured information symbols correspond with one another between their position in the natural order and their position in the interleaved order.

3. The method according to claim 1 , wherein the inter-layer adjustment values T l makes the positions of the most fragile non-punctured information symbols correspond with the positions of the least fragile non-punctured information symbols,

the degree of fragility of the positions being determined by comparing the distance spectra of the elementary codes obtained in puncturing each of the non-punctured information symbols one by one, the least fragile position corresponding to the spectrum having the greatest minimum Hamming distance and the lowest multiplicity and the most fragile position corresponding to the spectrum having the smallest minimum Hamming distance and the greatest multiplicity,

the multiplicity corresponding to the number of words of an elementary code at a distanced.

4. The method according to claim 3 , wherein the degrees of fragility of the positions having the same number of punctured redundancy symbols are determined on the basis of at least one comparison of the distance spectra of the elementary codes obtained by puncturing non-punctured redundancy symbols one by one, the least fragile position corresponding to the spectrum having the greatest minimum Hamming distance and the lowest multiplicity, and the most fragile position corresponding to the spectrum having the lowest minimum Hamming distance and the greatest multiplicity.

5. The method according to claim 1 , wherein the inter-layer adjustment values T l makes the positions of the most fragile punctured information symbols correspond with the positions of the least fragile punctured information symbols,

the degree of fragility of the positions being determined as a function of the number of punctured redundancy symbols, the least fragile positions being those for which no redundancy symbol is punctured and the most fragile positions being those for which all the redundancy symbols are punctured.

6. The method according to claim 5 , wherein the degrees of fragility of the positions having the same number of punctured redundancy symbols are determined on the basis of at least one comparison of the distance spectra of the elementary codes obtained by puncturing non-punctured redundancy symbols one by one, the least fragile position corresponding to the spectrum having the greatest minimum Hamming distance and the lowest multiplicity, and the most fragile position corresponding to the spectrum having the lowest minimum Hamming distance and the greatest multiplicity.

7. The method according to claim 1 , wherein the adjustment parameters of the interleaving function are determined as a function of predefined values of the minimum cumulative spatial distance S min and of the length of the minimum correlation cycle G min of the interleaver for at least one interleaver period P,

the length of the minimum correlation cycle G min of the interleaver corresponding to the length of the shortest correlation cycle of the graph of correlation between the input message, in the natural order, and the interleaved input message in the interleaved order.

8. The method according to claim 7 , wherein the predefined value of the minimum cumulative spatial distance S min of the interleaver is smaller than or equal to the greatest integer smaller than the square root of twice the length K of the input digital message S min =└√{square root over (2K)}┘, and the predefined value of the length of the minimum correlation cycle G min of the interleaver is smaller than or equal to Moore's theoretical limit ∈2 log 3 (K)┘.

9. The method according to claim 1 , wherein the period P of the interleaver is chosen to ensure a minimum cumulative spatial distance value S min of the interleaver greater than or equal to the minimum cumulative spatial distance of a regular interleaver whose interleaving function is Π(i)=Pi mod K.

10. The method according to claim 1 , wherein the two elementary codes of the first and second encoders of the turbo-encoder are identical.

11. The method according to claim 1 , wherein the elementary codes of the first and second encoders of the turbo-encoder are circular.

12. The method according to claim 1 wherein the puncturing period is a divider of the length of the input digital message.

13. A non-transitory computer-readable medium comprising a computer program stored thereon and comprising instructions for implementing a method of encoding when this the instructions are executed by a processor of a turbo-encoder, the method comprising:

encoding an input digital message bearing K information symbols using the turbo-encoder, the turbo-encoder forming a turbocode and comprising an interleaver and first and second encoders for encoding according to at least one elementary code and delivering said information symbols and redundancy symbols,

wherein, with a puncturing of the symbols delivered by the turbo-encoder being done according to at least one periodic puncturing pattern of a length N, defining the puncturing period, said interleaver distributes the information symbols of said input message into Q layers of the interleaved input message in complying with an interleaving function defined from said at least one puncturing pattern, according to the relationship:

π( i )= Pi+S ( i mod Q )mod K=Pi +( T l +A l Q )mod K

with:

i=0, . . . , K−1 being the position of an information symbol in said interleaved input message, in the interleaved order and π(i) the position of said information symbol in said input message, in the natural order;

P an integer value co-prime with the length K of said input message, called an interleaver period;

S(i mod Q)=S(l)=T l +A l Q are the parameters of adjustment of the interleaving function, with l=0, . . . , Q−1 the layer number;

Q a degree of disorder inserted into the interleaver, corresponding to the number of layers, such that Q=qN, with q≥1 being an integer and Q being a divider of K;

T l a value of inter-layer adjustment defined from said at least one puncturing pattern; and A l a value of intra-layer adjustment.

14. A turbo-encoder device comprising:

a processor; and

a non-transitory computer-readable medium comprising instructions stored thereon, which when executed by the processor configure the turbo-encoder device to:

encode an input digital message bearing K information symbols using an interleaver and first and second encoders for encoding according to at least one elementary code, and delivering said information symbols and redundancy symbols,

wherein a puncturing of the symbols delivered by said turbo-encoder being done according to at least one periodic puncturing pattern of a length N, defining the puncturing period, said interleaver distributes the information symbols of said input message in Q layers of the interleaved input message in complying with an interleaving function defined from said at least one puncturing pattern, according to the relationship:

π( i )= Pi+S ( i mod Q )mod K=Pi+S ( l )mod K=Pi +( T l +A l Q )mod K

with:

i=0, . . . , K−1 being the position of an information symbol in said interleaved input message, in the interleaved order and π(i) the position of said information symbol in said input message, in the natural order;

P an integer value co-prime with the length K of said input message, called an interleaver period;

S(i mod Q)=S(l)=T l +A l Q the parameters of adjustment of the interleaving function, with l=0, . . . , Q−1 the layer number;

Q a degree of disorder inserted into the interleaver, corresponding to the number of layers, such that Q=qN, with q≥1 being an integer and Q being a divider of K;

T l is a value of inter-layer adjustment defined from said at least one puncturing pattern; and

A l a value of intra-layer adjustment.