Enhanced Recursive Reed-Muller Erasure Decoding

TL;DR

This paper introduces an efficient encoding and decoding scheme for Reed-Muller codes on packet erasure channels, achieving near-ML performance with lower computational cost, especially for high-rate codes.

Contribution

It proposes a novel recursive decoding method based on Plotkin construction that improves speed and performance over generic decoding methods.

Findings

Achieves near-ML decoding performance at reduced computational cost

Significantly faster decoding for high-rate Reed-Muller codes

Outperforms generic decoding methods in erasure channels

Abstract

Recent work have shown that Reed-Muller (RM) codes achieve the erasure channel capacity. However, this performance is obtained with maximum-likelihood decoding which can be costly for practical applications. In this paper, we propose an encoding/decoding scheme for Reed-Muller codes on the packet erasure channel based on Plotkin construction. We present several improvements over the generic decoding. They allow, for a light cost, to compete with maximum-likelihood decoding performance, especially on high-rate codes, while significantly outperforming it in terms of speed.