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.

翻译：通用的低密度对等检查( GLDPC) 代码是一个代码类别, 常规的低密度对等检查( LDPC) 代码中单一对等检查节点由线性代码替换, 且对等检查限制较高 。 在本文中, 我们引入了一种新的方法, 构建 GLDPC 代码, 以插入部分剂量的通用检查节点 。 虽然常规的 Protograph GLDPC 代码用通用检查节点取代程序检查节点, 新的 GLDPC 代码通过添加通用检查节点, 部分使用选定的变量节点, 以拥有更高自由度的变量节点, 称部分使用 GLDPC (PD- GLDPC) 代码。 拟议的PD- GLDPC 代码可以进行更准确的扩展信息传输节点( 常规 GIT ) 分析, 和 doping gLD 代码可以用普通的 Oral- DLD 代码 来优化常规的运行率 。