Deep Learning-Based Belief Propagation Algorithm over Non-Binary Finite Fields

In this paper, we present a deep learning method for improving the belief propagation algorithm over non-binary Galois fields. The method is based on the deep unfolding structure of the factor graph representing LDPC matrix where the inference iterations according to Hadamard transform belief propagation algorithm are translated into layers of the neural networks. Afterwards, we introduce genetic algorithm to optimize the weights of the neural networks. The trained neural networks render much better performances than conventional belief propagation algorithms for both decoding of linear block codes and the compressed sensing reconstructions. The loss in terms of training process are also depicted, which show that the algorithm can converge after acceptable times of training.