Construction of Protograph-Based Partially Doped Generalized LDPC Codes

Abstract

In this paper, we propose a new code design technique, called partial doping, for protographbased 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).INDEX TERMS Generalized low-density parity-check (GLDPC) codes, partial doping, partially doped GLDPC (PD-GLDPC) codes, protograph, protograph extrinsic information transfer (PEXIT), typical minimum distance.

The Cycle-Concentrating PEG Algorithm for Protograph Generalized LDPC Codes

“…The CC-PEG codes lifted from the larger protographs P 4 and P 5 [16] with more edges show much larger gains, as shown in Fig. 9.…”

“…Since there has been no research conducted on lifting methods specially tailored for GLDPC codes, we choose the most commonly used lifting algorithms, PEG and QC-PMP, for comparison. The regular protograph P 1 and irregular protographs (16-1), (14-2) in [15], and ( 6), ( 5) in [16], which show near-capacity asymptotic performances, are employed to demonstrate the effectiveness of the CC-PEG algorithm over various protographs, lengths, and code rates. Denote the irregular protographs by P 2 -P 5 in the order written above.…”

“…Through extensive simulations, we find a superior ordering policy: i) First, sort out VNs in the degree ascending order, and then ii) place the doped VNs backward among the VNs with the same degree. As well-constructed protographs typically have higher-degree doped VNs than undoped VNs [15], [16], most doped VNs are still arranged at the back side in accordance with this ordering policy.…”

“…Extensive decoding simulations are conducted over both the binary erasure channel (BEC) and the additive white Gaussian noise (AWGN) channel using regular and irregular GLDPC protographs in [15] and [16], which have capacity-approaching performance. The results confirm that the CC-PEG algorithm achieves a significant coding gain compared to other existing lifting algorithms [9], [13], particularly for large protographs and moderate code lengths, where GLDPC codes are known to perform better than LDPC codes [5].…”

“…First, we propose the CC-PEG algorithm which is the first lifting algorithm specially designed for GLDPC codes. Although many studies have focused on the optimization of protograph GLDPC codes [15], [16], [17], a lifting method specialized for GLDPC codes has yet to be developed. The proposed algorithm can be applied to lift any GLDPC protograph with doped and undoped VNs.…”