High Girth Spatially-Coupled LDPC Codes with Hierarchical Structure

TL;DR

This paper presents a novel algorithm for constructing quasi-cyclic spatially-coupled LDPC codes with large girth and small constraint length, improving performance and hardware efficiency.

Contribution

It extends hierarchical QC LDPC code construction to spatially-coupled codes, enabling large girth with low lifting factors for better performance and implementation.

Findings

Achieves large girth with small lifting size.

Enables low-complexity code construction.

Extends hierarchical QC code design to SC codes.

Abstract

Quasi-cyclic (QC) low-density parity-check (LDPC) codes are a class of LDPC codes with a simple construction facilitating hardware implementation while achieving excellent performance. In this paper, we introduce an algorithm that constructs QC spatially-coupled (SC) LDPC codes with large girth while keeping the constraint length small. The algorithm offers a "protograph to basegraph" construction, focusing on finding small lifting sizes of QC codes while avoiding short cycles. This work extends the hierarchical quasi-cyclic (HQC) construction for block LDPC codes proposed by Wang et al. to the spatially coupled case. The construction is based on the cycle relevant matrix (CRM) derived from the periodic structure of time-invariant SC-LDPC codes. Numerical results show that the proposed algorithm effectively achieves the target girth with a small lifting factor, enabling low-complexity SC code construction.