Iterative Reed-Muller Decoding

TL;DR

This paper introduces a belief propagation decoding architecture for Reed-Muller codes that leverages their automorphism group, achieving near-ML performance with competitive complexity.

Contribution

It presents a novel BP decoding method for RM codes based on automorphisms, outperforming previous iterative decoders in error-rate performance.

Findings

Near-ML performance for RM(3,7)-code at BLER of 10^{-4}

Achieves best performance among iterative RM decoders to date

Competitive computational cost compared to existing schemes

Abstract

Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an open problem. In this work, we present a belief propagation (BP) decoding architecture for RM codes based on their rich automorphism group. The decoding algorithm can be seen as a generalization of multiple-bases belief propagation (MBBP) using polar BP as constituent decoders. We provide extensive error-rate performance simulations and compare our results to existing decoding schemes. We report a near-ML performance for the RM(3,7)-code (e.g., 0.05 dB away from the ML bound at BLER of $10^{-4}$) at a competitive computational cost. To the best of our knowledge, our proposed decoder achieves the best performance of all iterative RM decoders presented thus far.