Recursive projection-aggregation decoding of Reed-Muller codes

TL;DR

This paper introduces a recursive projection-aggregation decoding algorithm for Reed-Muller codes that outperforms polar code decoders at short lengths and can be efficiently parallelized.

Contribution

The paper presents a novel recursive decoding method for Reed-Muller codes that improves performance and extends to list-decoding, outperforming existing polar code decoders.

Findings

Outperforms polar code decoders in low and high rate regimes

Close to maximum likelihood decoding performance

Suitable for parallel implementation

Abstract

We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are lower-order RM codes), and aggregating the reconstructions (e.g., using majority votes). We further provide extensions of the algorithms using list-decoding. We run our algorithm for AWGN channels and Binary Symmetric Channels at the short code length ($\le 1024$) regime for a wide range of code rates. Simulation results show that in both low code rate and high code rate regimes, the new algorithm outperforms the widely used decoder for polar codes (SCL+CRC) with the same parameters. The performance of the new algorithm for RM codes in those regimes is in fact close to that of the maximal likelihood decoder. Finally, the new decoder naturally allows for parallel implementations.