New decoding scheme for LDPC codes based on simple product code structure

TL;DR

This paper introduces a novel LDPC decoding method leveraging simple product code structures, combining two soft-decision data sets to enhance error correction with minimal added complexity.

Contribution

It proposes a new LDPC decoding scheme based on product codes, analyzing its combined-decodability and demonstrating improved high-SNR error correction performance.

Findings

Achieves better error correction in high SNR regions

Uses simple algebraic codes as vertical codes to assist LDPC decoding

Offers low additional decoding complexity compared to conventional methods

Abstract

In this paper, a new decoding scheme for low-density parity-check (LDPC) codes using the concept of simple product code structure is proposed based on combining two independently received soft-decision data for the same codeword. LDPC codes act as horizontal codes of the product codes and simple algebraic codes are used as vertical codes to help decoding of the LDPC codes. The decoding capability of the proposed decoding scheme is defined and analyzed using the paritycheck matrices of vertical codes and especially the combined-decodability is derived for the case of single parity-check (SPC) and Hamming codes being used as vertical codes. It is also shown that the proposed decoding scheme achieves much better error-correcting capability in high signal to noise ratio (SNR) region with low additional decoding complexity, compared with a conventional decoding scheme.