New construction of partial geometries based on group divisible designs and their associated LDPC codes
New construction of partial geometries based on group divisible designs and their associated LDPC codes
复制标题
基于群可分设计及其相关LDPC码的部分几何新构造
DOI：
10.1016/j.phycom.2019.100970
复制
发表时间：
2020
影响因子：
2.2
通讯作者：
Zhu Hai
中科院分区：
文献类型：
--
作者：
Xu Hengzhou;Yu Zhongyang;Feng Dan;Zhu Hai
作为一个通用框架，部分几何在构建具有低错误本底的良好低密度奇偶校验（LDPC）码方面发挥着重要作用。 Q. Diao 等人确定了循环置换矩阵 (CPM) 的行列约束（RC 约束）数组的部分几何形状。在本文中，我们研究基于组可分设计 (GDD) 的 RC 约束矩阵的部分几何形状。从组合设计的角度来看，表明两类部分几何的存在分别相当于平衡不完全块设计（BIBD）和横向设计（TD）的存在。因此，提出了BIBD和TD的相关构造。此外，我们提出了一种利用 GDD 的可解析性来构造具有灵活码率和长度参数的 LDPC 码的方法。数值结果表明，所提出的 LDPC 码在加性高斯白噪声 (AWGN) 信道上的迭代解码下具有良好的性能。
As a general framework, partial geometries play an important role in constructing good low-density parity-check (LDPC) codes with low error-floors. Partial geometries from row–column constrained (RC-constrained) arrays of circulant permutation matrices (CPMs) have been determined by Q. Diao et al. In this paper, we study partial geometries from RC-constrained matrices based on group divisible designs (GDDs). From the combinational design perspective, it is shown that the existence of two classes of partial geometries is equivalent to the existence of balanced incomplete block designs (BIBDs) and transversal design (TDs), respectively. Therefore, relevant constructions of BIBDs and TDs are presented. Furthermore, we present a method for constructing LDPC codes with flexible code rate and length parameters by employing the resolvability of GDDs. Numerical results show that the proposed LDPC codes have good performance under iterative decoding over the additive white Gaussian noise (AWGN) channel.