Decoding Reed-Muller Codes with Successive Codeword Permutations

Abstract

This paper presents a novel successive factor-graph permutation (SFP) scheme that significantly improves the error-correction performance of Reed-Muller (RM) codes under successive-cancellation list (SCL) decoding. In particular, we perform maximum-likelihood decoding on the symmetry group of RM codes to carefully select a good factor-graph permutation on the fly. We further propose an SFP-aided fast SCL decoding that significantly reduces the decoding latency while preserving the errorcorrection performance of the code. The simulation results show that for the third and fourth order RM codes of length 256, the proposed decoder reduces up to 85% of the memory consumption, 78% of the decoding latency, and more than 99% of the computational complexity of the state-of-the-art recursive projection-aggregation decoder at the frame error rate of 10 −3 .