Affine Subcode Ensemble Decoding of Linear Block Codes

TL;DR

This paper introduces affine subcode ensemble decoding (aSCED), a novel decoding scheme for linear block codes that improves error correction and reduces latency by using an ensemble of decoders on affine subcodes.

Contribution

The work generalizes subcode ensemble decoding to include affine subcodes, simplifying ensemble design and achieving near-ML performance with low complexity.

Findings

aSCED outperforms existing ensemble decoding schemes in error correction.

For a BCH code, aSCED achieves near-maximum likelihood performance with only 64 BP paths.

Monte-Carlo simulations confirm improved performance on LDPC and BCH codes.

Abstract

In the short block length regime, ensemble decoding schemes with their inherently parallel structure can improve error correction performance and reduce latency compared to stand-alone suboptimal decoders such as belief propagation (BP). In this work, we introduce affine subcode ensemble decoding (aSCED), which uses an ensemble of decoders operating on linear block codes and both linear and strictly affine subcodes. This generalizes the recently proposed subcode ensemble decoding (SCED), which is restricted to linear subcodes. We derive BP update rules for affine subcodes and show that aSCED simplifies ensemble design compared to SCED, multiple bases BP, and automorphism ensemble decoding. Monte-Carlo simulations of two low-density parity-check codes and two Bose-Chaudhuri-Hocquenghem (BCH) codes demonstrate improved error correction performance of aSCED over competing existing ensemble schemes. Notably, for one BCH code, when combining ensemble design with algorithms for constructing high-performance parity-check matrices, aSCED achieves near-maximum likelihood performance using only 64 BP decoding paths.