Generalized reliability-based syndrome decoding for LDPC codes

TL;DR

This paper introduces a generalized syndrome decoding method that cascades with belief propagation or min-sum decoding for LDPC codes, improving decoding performance and complexity tradeoffs.

Contribution

It extends ordered statistic decoding to probability domain and normalized/offset min-sum decoding, offering a new cascade decoding approach for LDPC codes.

Findings

Cascade decoding outperforms BP alone in performance.

Generalized OSD reduces complexity without performance loss.

Effective error pattern selection improves decoding efficiency.

Abstract

Aiming at bridging the gap between the maximum likelihood decoding (MLD) and the suboptimal iterative decodings for short or medium length LDPC codes, we present a generalized ordered statistic decoding (OSD) in the form of syndrome decoding, to cascade with the belief propagation (BP) or enhanced min-sum decoding. The OSD is invoked only when the decoding failures are obtained for the preceded iterative decoding method. With respect to the existing OSD which is based on the accumulated log-likelihood ratio (LLR) metric, we extend the accumulative metric to the situation where the BP decoding is in the probability domain. Moreover, after generalizing the accumulative metric to the context of the normalized or offset min-sum decoding, the OSD shows appealing tradeoff between performance and complexity. In the OSD implementation, when deciding the true error pattern among many candidates, an alternative proposed proves to be effective to reduce the number of real additions without performance loss. Simulation results demonstrate that the cascade connection of enhanced min-sum and OSD decodings outperforms the BP alone significantly, in terms of either performance or complexity.