Abstract: A method and a system are provided in which a message is encoded, by a neural encoder, to generate a codeword having a first length corresponding to a first code rate of the neural encoder. A number of components of the codeword corresponds to the first code rate. At least one of repeating the components or puncturing at least one of the components is performed to generate a rate-matched codeword having a second length corresponding to a second code rate. The rate-matched codeword is estimated and modified to generate an estimated codeword having the first length corresponding to the first code rate of a neural decoder. The estimated codeword is decoded, by the neural decoder, to generate an estimated message.

Abstract: A processing circuit implements: an encoder configured to: supply k symbols of original data to a neural product encoder including M neural encoder stages, a j-th neural encoder stage including a j-th neural network configured by j-th parameters to implement an (nj,kj) error correction code (ECC), where nj is a factor of n and kj is a factor of k; and output n symbols representing the k symbols of original data encoded by an error correcting code; or a decoder configured to supply n symbols of a received message to a neural product decoder including neural decoder stages grouped into a l pipeline stages, an i-th pipeline stage of the neural product decoder including M neural decoder stages, a j-th neural decoder stage comprising a j-th neural network configured by j-th parameters to implement an (nj,kj) ECC; and output k symbols decoded from the n symbols of the received message.