Two-Bit Bit Flipping Decoding of LDPC Codes

TL;DR

This paper introduces a novel two-bit bit flipping decoding algorithm for LDPC codes that enhances error correction capability and outperforms traditional algorithms like Gallager A/B and min-sum at lower complexity, with potential to approach belief propagation performance.

Contribution

The paper presents a new two-bit variable node decoding algorithm that significantly improves error correction and complexity over existing bit flipping methods.

Findings

Increases guaranteed error correction by at least a factor of 2.

Outperforms Gallager A/B and min-sum algorithms in error correction.

Potential to approach belief propagation performance in the error floor region.

Abstract

In this paper, we propose a new class of bit flipping algorithms for low-density parity-check (LDPC) codes over the binary symmetric channel (BSC). Compared to the regular (parallel or serial) bit flipping algorithms, the proposed algorithms employ one additional bit at a variable node to represent its "strength." The introduction of this additional bit increases the guaranteed error correction capability by a factor of at least 2. An additional bit can also be employed at a check node to capture information which is beneficial to decoding. A framework for failure analysis of the proposed algorithms is described. These algorithms outperform the Gallager A/B algorithm and the min-sum algorithm at much lower complexity. Concatenation of two-bit bit flipping algorithms show a potential to approach the performance of belief propagation (BP) decoding in the error floor region, also at lower complexity.