Decoding Reed-Muller Codes with Successive Factor-Graph Permutations

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 error-correction 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 $10^{-3}$.