Improved Iterative Hard- and Soft-Reliability Based Majority-Logic Decoding Algorithms for Non-Binary Low-Density Parity-Check Codes

TL;DR

This paper introduces two novel improvements to majority-logic decoding algorithms for non-binary LDPC codes, enhancing error performance, reducing iterations, lowering error floors, and maintaining low complexity.

Contribution

The paper proposes a new reliability update method and a re-selection scheme, significantly improving decoding performance and error floors for non-binary LDPC codes.

Findings

Better error performance with fewer iterations

Lower error floors for low column weight codes

Reduced computational complexity

Abstract

Non-binary low-density parity-check (LDPC) codes have some advantages over their binary counterparts, but unfortunately their decoding complexity is a significant challenge. The iterative hard- and soft-reliability based majority-logic decoding algorithms are attractive for non-binary LDPC codes, since they involve only finite field additions and multiplications as well as integer operations and hence have significantly lower complexity than other algorithms. In this paper, we propose two improvements to the majority-logic decoding algorithms. Instead of the accumulation of reliability information in the existing majority-logic decoding algorithms, our first improvement is a new reliability information update. The new update not only results in better error performance and fewer iterations on average, but also further reduces computational complexity. Since existing majority-logic decoding algorithms tend to have a high error floor for codes whose parity check matrices have low column weights, our second improvement is a re-selection scheme, which leads to much lower error floors, at the expense of more finite field operations and integer operations, by identifying periodic points, re-selecting intermediate hard decisions, and changing reliability information.