Sparse Multi-Decoder Recursive Projection Aggregation for Reed-Muller Codes

TL;DR

This paper introduces a sparse multi-decoder recursive projection aggregation algorithm for Reed-Muller codes that significantly reduces computational complexity while maintaining near-optimal decoding performance.

Contribution

It proposes a novel sparse RPA decoding method that cuts computational costs by up to 80% with minimal performance degradation.

Findings

Reduces RPA decoding computations by up to 80%.

Maintains performance close to original RPA decoder.

Uses CRC for effective codeword selection.

Abstract

Reed-Muller (RM) codes are one of the oldest families of codes. Recently, a recursive projection aggregation (RPA) decoder has been proposed, which achieves a performance that is close to the maximum likelihood decoder for short-length RM codes. One of its main drawbacks, however, is the large amount of computations needed. In this paper, we devise a new algorithm to lower the computational budget while keeping a performance close to that of the RPA decoder. The proposed approach consists of multiple sparse RPAs that are generated by performing only a selection of projections in each sparsified decoder. In the end, a cyclic redundancy check (CRC) is used to decide between output codewords. Simulation results show that our proposed approach reduces the RPA decoder's computations up to $80\%$ with negligible performance loss.