Method for decoding, computer program product, and device

A method for decoding at least M0 symbols X10, . . . , XM00 received from a transmitter through a wireless communication medium, said received symbols representing symbols encoded by an encoder E of the transmitter, said method comprising:

• inputting in a decoder the M0 symbols X10, . . . , XM00 said decoder comprising an artificial neural network system, wherein at least an activation function of the artificial neural network system is a multiple level activation function,
• wherein the encoder E comprises a Lattice encoder, wherein inputs of the Lattice encoder being inputs of the encoder E,
• wherein the decoder is defined as a function F which is defined by N sets of functions F1i, . . . , FMii, with i from 1 to N, Fmi(X1i-1, . . . , XMi-1i-1)=ƒmi(Σk=1Mi-1 wk,mi-1×Xki-1+βmi), with F(X10, . . . , XM00)=[F1N(X1N-1, . . . , XMN-1N-1), . . . , FMNN(X1N-1, . . . , XMN-1N-1)], where, Xmi-1 are respectively the outputs of the functions Fmi-1, Xmi-1=Fmi-1(X1i-2, . . . , XMi-1i-2) of the (i−1)-th set, each ƒmi is either an artificial neural network activation function or an identity function, at least one of the ƒmi is not an identity function and w1,mi-1, . . . , wMi-1,m′i-1, βmi are real number parameters,
• wherein at least one of the functions ƒmi with m from 1 to Mi and i from 1 to N−1 is a multiple level activation function.

A device for receiving M0 symbols X10, . . . , XM00 from a transmitter through a wireless communication medium, said received symbols representing symbols encoded by an encoder E of the transmitter, the device comprises:

• a reception module;
• and
• a decoder, said decoder comprising an artificial neural network system, wherein at least an activation function of the artificial neural network system is a multiple level activation function,
• wherein the encoder E comprises a Lattice encoder, wherein inputs of the Lattice encoder being inputs of the encoder E,
• wherein the decoder is defined as a function F which is defined by N sets of functions F1i, . . . , FMii, with i from 1 to N, Fmi(X1i-1, . . . , XMi-1i-1)=ƒmi(Σk=1Mi-1 wk,mi-1×Xki-1+βmi), with F(X10, . . . , XM00)=[F1N(X1N-1, . . . , XMN-1N-1)], . . . , FMNN(X1N-1, . . . , XMN-1N-1)), where, Xmi-1 are respectively the outputs of the functions Fmi-1, Xmi-1=Fmi-1(X1i-2, . . . , XMi-1i-2) of the (i−1)-th set, each ƒmi is either an artificial neural network activation function or an identity function, at least one of the ƒmi is not an identity function and w1,mi-1, . . . , wMi-1,m′i-1, βmi are real number parameters,
• wherein at least one of the functions ƒmi with m from 1 to Mi and i from 1 to N−1 is a multiple level activation function.