Subcode Ensemble Decoding of Linear Block Codes

TL;DR

This paper introduces subcode ensemble decoding (SCED), a novel approach for short block length LDPC codes that improves decoding performance without complex searches or automorphism group knowledge.

Contribution

The paper proposes SCED, a new ensemble decoding method for short LDPC codes that enhances error correction and reduces decoding complexity.

Findings

SCED outperforms stand-alone decoding and automorphism ensemble decoding in simulations.

SCED does not require NP-complete searches for low-weight dual codewords.

SCED is effective for short block length LDPC codes with unknown automorphism groups.

Abstract

Low-density parity-check (LDPC) codes together with belief propagation (BP) decoding yield exceptional error correction capabilities in the large block length regime. Yet, there remains a gap between BP decoding and maximum likelihood decoding for short block length LDPC codes. In this context, ensemble decoding schemes yield both reduced latency and good error rates. In this paper, we propose subcode ensemble decoding (SCED), which employs an ensemble of decodings on different subcodes of the code. To ensure that all codewords are decodable, we use the concept of linear coverings and explore approaches for sampling suitable ensembles for short block length LDPC codes. Monte-Carlo simulations conducted for three LDPC codes demonstrate that SCED improves decoding performance compared to stand-alone decoding and automorphism ensemble decoding. In particular, in contrast to existing schemes, e.g., multiple bases belief propagation and automorphism ensemble decoding, SCED does not require the NP-complete search for low-weight dual codewords or knowledge of the automorphism group of the code, which is often unknown.