A Tree Search Approach for Maximum-Likelihood Decoding of Reed-Muller Codes

TL;DR

This paper introduces a low-complexity tree search method for maximum-likelihood decoding of Reed-Muller codes, using DFS and BFS strategies with a bit-flipping metric to improve efficiency and reduce node visits.

Contribution

It presents a novel tree search decoding algorithm for Reed-Muller codes that improves efficiency over existing methods by reducing node visits using BFS and a new bit-flipping metric.

Findings

BFS scheme reduces average node visits compared to previous methods.

The proposed algorithm achieves ML decoding performance with lower complexity.

Enhancements further decrease the number of node visits during decoding.

Abstract

A low-complexity tree search approach is presented that achieves the maximum-likelihood (ML) decoding performance of Reed-Muller (RM) codes. The proposed approach generates a bit-flipping tree that is traversed to find the ML decoding result by performing successive-cancellation decoding after each node visit. A depth-first search (DFS) and a breadth-first search (BFS) scheme are developed and a log-likelihood-ratio-based bit-flipping metric is utilized to avoid redundant node visits in the tree. Several enhancements to the proposed algorithm are presented to further reduce the number of node visits. Simulation results confirm that the BFS scheme provides a lower average number of node visits than the existing tree search approach to decode RM codes.