Short Regular Girth-8 QC-LDPC Codes From Exponent Matrices with Vertical Symmetry

TL;DR

This paper introduces a new framework based on vertical symmetry for constructing short girth-8 QC-LDPC codes, offering explicit and search-based methods that outperform existing benchmarks in code length while maintaining or improving performance.

Contribution

The paper presents a novel vertical symmetry-based construction framework for short girth-8 QC-LDPC codes, including explicit and search methods that produce shorter codes with comparable or better performance.

Findings

Shorter codes achieved compared to benchmarks.

Explicit constructions for specific column weights.

Search-based method effectively finds optimal codes.

Abstract

To address the challenge of constructing short girth-8 quasi-cyclic (QC) low-density parity-check (LDPC) codes, a novel construction framework based on vertical symmetry (VS) is proposed. Basic properties of the VS structure are presented. With the aid of these properties, existing explicit constructions for column weights from three to five which can be transformed into the VS structure are sorted out. Then two novel explicit constructions with the VS structure which guarantee short codes are presented for column weights of three and six. Moreover, an efficient search-based method is also proposed to find short codes with the VS structure. Compared with the state-of-the-art benchmarks, both the explicit constructions and the search-based method presented in this paper can provide shorter codes for most cases. Simulation results show that the new shorter codes can perform almost the same as or better than the longer existing counterparts. Thus, the new shorter codes can fit better with the low-latency requirement for modern communication systems.