Semi-Deterministic Subspace Selection for Sparse Recursive Projection-Aggregation Decoding of Reed-Muller Codes

TL;DR

This paper introduces a semi-deterministic subspace selection method for sparse RPA decoding of Reed-Muller codes, significantly improving decoding performance and reducing complexity compared to existing SRPA approaches.

Contribution

It proposes a novel semi-deterministic subspace selection technique that enhances decoding accuracy and decreases computational complexity in sparse RPA decoding of Reed-Muller codes.

Findings

Decoding performance improved by up to 0.2 dB over SRPA.

Decoding complexity reduced by up to 81% for RM codes of order r≥3.

Performance gains achieved on AWGN channels.

Abstract

Recursive projection aggregation (RPA) decoding as introduced in [1] is a novel decoding algorithm which performs close to the maximum likelihood decoder for short-length Reed-Muller codes. Recently, an extension to RPA decoding, called sparse multi-decoder RPA (SRPA), has been proposed [2]. The SRPA approach makes use of multiple pruned RPA decoders to lower the amount of computations while keeping the performance loss small compared to RPA decoding. However, the use of multiple sparse decoders again increases the computational burden. Therefore, the focus is on the optimization of sparse single-decoder RPA decoding to keep the complexity small. In this paper, a novel method is proposed, to select subsets of subspaces used in the projection and aggregation step of SRPA decoding in order to decrease the decoding error probability on AWGN channels. The proposed method replaces the random selection of subspace subsets with a semi-deterministic selection method based on a figure of merit that evaluates the performance of each subspace. Our simulation results show that the semi-deterministic subspace selection improves the decoding performance up to $0.2\,\text{dB}$ compared to SRPA. At the same time, the complexity of SRPA decoding for RM codes of order $r\geq 3$ is reduced by up to 81% compared to SRPA.