Method for generating a signal by means of a turbo-encoder, and corresponding device and computer program

A non-transitory computer-readable medium comprising instructions stored therein, which when executed by a processor of a coding device, configure the coding device to:

• receive an input digital message comprising a set of information symbols;
• turbo-code the set of information symbols comprised in the input digital message, the information symbols belonging to a Galois field of cardinal q, denoted GF(q), with q>2, wherein the turbo-coding implements a non-binary turbo-code type error correcting code to obtain redundancy symbols and comprises:
• encoding said set of information symbols by a first encoder of the coding device to generate a first set of redundancy symbols;
• interleaving said set of information symbols using an interleaver of the coding device to generate a set of interleaved information symbols;
• encoding said set of interleaved information symbols by a second encoder of the coding device to generate a second set of redundancy symbols;
• mapping the information and redundancy symbols onto modulation symbols associated with a constellation of order p, an information or redundancy symbol being mapped onto n modulation symbols, with n≥2, the order p of the constellation being less than the cardinal q of the Galois field to which said information symbols belong;
• applying a bijective transformation to said information symbols using a processor of the coding device before and/or after said interleaving, said transformation modifying a value of at least two of said information symbols prior to the coding of said information symbols by the first encoder and/or the second encoder, the bijective transformation being defined such that every input of a set of q elements of GF(q) has a unique output in the set of q elements of GF(q) by the bijective transformation and every output of the set of q elements of GF(q) has a unique antecedent in the set of q elements of GF(q), said transformation taking into account said constellation;
• generating an output signal representing a code word which comprises the set of information symbols and the first and second sets of redundancy symbols;
• and
• transmitting the output signal in a communications system.

A method performed by a coding device, the method comprising:

• receiving an input digital message comprising a set of information symbols;
• turbo-coding the set of information symbols comprised in the input digital message, the information symbols belonging to a Galois field of cardinal q, denoted GF(q), with q>2, wherein the turbo-coding implements a non-binary turbo-code type error correcting code to obtain redundancy symbols and comprises:
• encoding said set of information symbols by a first encoder of the coding device to generate a first set of redundancy symbols,
• interleaving said set of information symbols using an interleaver of the coding device to generate a set of interleaved information symbols;
• encoding said set of interleaved information symbols by a second encoder of the coding device to generate a second set of redundancy symbols;
• and
• applying a bijective transformation to said information symbols using a processor of the coding device before and/or after said interleaving, said transformation modifying a value of at least two of said information symbols prior to the coding of said information symbols by the first encoder and/or the second encoder, the bijective transformation being defined such that every input of a set of q elements of GF(q) has a unique output in the set of q elements of GF(q) by the bijective transformation and every output of the set of q elements of GF(q) has a unique antecedent in the set of q elements of GF(q);
• generating an output signal representing a code word which comprises the set of information symbols and the first and second sets of redundancy symbols;
• and
• transmitting the output signal in a communications system,
• wherein:
• said transformation generates a minimum dispersion Δmin between two information symbols Si, Sj among said information symbols greater than a selection threshold, such that:
• Δmin=min Δ(Si,Sj)
• with:
• Δ(Si,Sj)=D(Si,Sj)+D(T(Si),T(Sj))
• D(Si,Sj) being a distance between said information symbols Si, Sj before transformation,
• D(T(Si),T(Sj)) being a distance between said information symbols Si, Sj after transformation by the function T;
• the method comprises mapping the information and redundancy symbols onto modulation symbols associated with a constellation of order p equal to the cardinal q of the Galois field to which said information symbols belong, an information or redundancy symbol being mapped onto a single modulation symbol, and said transformation takes into account said constellation;
• and
• dispersion between two information symbols Si, Sj is expressed in the form:
• Δ(Si,Sj)=deuc2(Sim,Sjm)+deuc2(T(Si)m,T(Sj)m)
• with:
• deuc2(Sim,Sjm)=(Isim−Isjm)2+(Qsim−Qsjm)2 being the square of the Euclidean distance between the modulation symbols Sim, Sjm onto which said information symbols Si, Sj are mapped before transformation;
• deuc2(T(Si)m,T(Sj)m)=(IT(Si)m−IT(Sj)m)2+(QT(Si)m−QT(Sj)m)2 being the square of the Euclidean distance between the modulation symbols T(Si)m, T(Sj)m onto which said information symbols Si, Sj are mapped after transformation;
• Ix and Qx are the in-phase and quadrature components of a signal x in the considered constellation.

A method performed by a coding device, the method comprising:

• receiving an input digital message comprising a set of information symbols;
• turbo-coding the set of information symbols comprised in the input digital message, the information symbols belonging to a Galois field of cardinal q, denoted GF(q), with q>2, wherein the turbo-coding implements a non-binary turbo-code type error correcting code to obtain redundancy symbols and comprises:
• encoding said set of information symbols by a first encoder of the coding device to generate a first set of redundancy symbols,
• interleaving said set of information symbols using an interleaver of the coding device to generate a set of interleaved information symbols;
• encoding said set of interleaved information symbols by a second encoder of the coding device to generate a second set of redundancy symbols;
• and
• applying a bijective transformation to said information symbols using a processor of the coding device before and/or after said interleaving, said transformation modifying a value of at least two of said information symbols prior to the coding of said information symbols by the first encoder and/or the second encoder, the bijective transformation being defined such that every input of a set of q elements of GF(q) has a unique output in the set of q elements of GF(q) by the bijective transformation and every output of the set of q elements of GF(q) has a unique antecedent in the set of q elements of GF(q);
• generating an output signal representing a code word which comprises the set of information symbols and the first and second sets of redundancy symbols;
• and
• transmitting the output signal in a communications system,
• wherein:
• the method comprises mapping the information and redundancy symbols onto modulation symbols associated with a constellation of order p, an information or redundancy symbol being mapped onto n modulation symbols, with n≥2, the order p of the constellation being less than the cardinal q of the Galois field to which said information symbols belong;
• and
• said transformation takes into account said constellation.