Construction of Protograph-Based Partially Doped Generalized LDPC Codes

TL;DR

This paper introduces a novel construction method for generalized LDPC codes called partially doped GLDPC (PD-GLDPC), which enhances analysis accuracy and code performance by adding generalized check nodes and doping selected variable nodes.

Contribution

The paper proposes a new PD-GLDPC construction method that allows finer doping granularity, improved EXIT analysis, and higher code rates compared to conventional GLDPC codes.

Findings

PD-GLDPC codes enable more accurate EXIT analysis.

Proposed codes achieve higher rates than conventional GLDPC.

Block error rate performance outperforms existing LDPC codes under similar conditions.

Abstract

A generalized low-density parity-check (GLDPC) code is a class of codes, where single parity check nodes in a conventional low-density parity-check (LDPC) code are replaced by linear codes with higher parity check constraints. In this paper, we introduce a new method of constructing GLDPC codes by inserting the generalized check nodes for partial doping. While the conventional protograph GLDPC code dopes the protograph check nodes by replacing them with the generalized check nodes, a new GLDPC code is constructed by adding the generalized check nodes and partially doping the selected variable nodes to possess higher degrees of freedom, called a partially doped GLDPC (PD-GLDPC) code. The proposed PD-GLDPC codes can make it possible to do more accurate extrinsic information transfer (EXIT) analysis and the doping granularity can become finer in terms of the protograph than the conventional GLDPC code. We also propose the constraint for the typical minimum distance of PD-GLDPC codes and prove that the PD-GLDPC codes satisfying this condition have the linear minimum distance growth property. Furthermore, we obtain the threshold optimized protograph for both regular and irregular ensembles of the proposed PD-GLDPC codes over the binary erasure channel (BEC). Specifically, we propose the construction algorithms for both regular and irregular protograph-based PD-GLDPC codes that enable the construction of GLDPC codes with higher rates than the conventional ones. The block error rate performance of the proposed PD-GLDPC code shows that it has a reasonably good waterfall performance with low error floor and outperforms other LDPC codes for the same code rate, code length, and degree distribution.