Construction of Protograph-Based Partially Doped Generalized LDPC Codes

Abstract

In this paper, we propose a new code design technique, called partial doping, for protograph-based generalized low-density parity-check (GLDPC) codes. While the conventional construction method of protograph-based GLDPC codes is to replace some single parity-check (SPC) nodes with generalized constraint (GC) nodes applying to multiple variable nodes (VNs) that are connected in the protograph, the proposed technique can select any VNs in the protograph to be protected by GC nodes. In other words, the partial doping technique facilitates finer tuning of doping, which in turn enables a sophisticated code optimization with higher degree of freedom. We construct the proposed partially doped GLDPC (PD-GLDPC) codes using the partial doping technique and optimize the PD-GLDPC codes by the protograph extrinsic information transfer (PEXIT) analysis. In addition, we propose a condition guaranteeing the linear minimum distance growth of the PD-GLDPC codes and use the condition for the optimization. Experimental results show that the optimized PD-GLDPC codes outperform the conventional GLDPC codes and have competitive performance compared to the state-of-the-art protograph-based LDPC codes without the error floor phenomenon over the binary erasure channel (BEC).

Keywords

• Generalized low-density parity-check (GLDPC) codes
• partial doping
• partially doped GLDPC (PD-GLDPC) codes
• protograph
• protograph extrinsic information transfer (PEXIT)
• typical minimum distance