A Deep Learning Assisted Node-Classified Redundant Decoding Algorithm for BCH Codes

This paper proposes a node-classified redundant decoding (NC-RD) algorithm based on the received sequence's channel reliability for high-density parity-check (HDPC) codes. Two preprocessing steps are proposed prior decoding. The variable nodes of the parity-check matrix are firstly classified by the k -median algorithm based on the number of shortest cycles associated with each variable node before decoding. Then, by searching among the automorphism group of the HDPC codes, we generate a list of permutations for bit positions by computing and sorting the permutation reliability metrics. The redundant decoder conducts the message-passing decoding according to the sorted permutations, which limit the unreliable information propagation for each permutation. Besides proposing a list decoding algorithm on top of the NC-RD algorithm to augment the decoder's performance, we show that the NC-RD algorithm can be transformed into a neural network system. More specifically, multiplicative tuneable weights are attached to the decoding messages to optimize the decoding performance. Simulation results of BCH codes over the AWGN channels show that the NC-RD algorithm provides a performance gain compared to the random redundant decoding algorithm. Additional decoding performance gain can be obtained by both the list decoding method and the neural network “learned” NC-RD algorithm.