Cyclic and Quasi-Cyclic LDPC Codes on Constrained Parity-Check Matrices and Their Trapping Sets
Cyclic and Quasi-Cyclic LDPC Codes on Constrained Parity-Check Matrices and Their Trapping Sets
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DOI：
10.1109/tit.2011.2179842
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发表时间：
2012-05
影响因子：
2.5
通讯作者：
Qin Huang;Qiuju Diao;Shu Lin;K. Abdel-Ghaffar
中科院分区：
文献类型：
--
作者：
Qin Huang;Qiuju Diao;Shu Lin;K. Abdel-Ghaffar
本文研究了循环码和准循环码，特别是低密度奇偶校验（LDPC）码的构造和结构分析。它由三部分组成。第一部分表明，由循环形式的奇偶校验矩阵给出的循环码可以分解成各种长度和速率的后代循环码和准循环码。这些后代码的一些基本的结构性质的发展，包括一个循环后代码的生成多项式的根的特征。本文的第二部分表明，循环和准循环后裔LDPC码可以从循环有限几何LDPC码使用的结果在第一部分的文件。这扩大了循环LDPC码的库。论文的第三部分分析了校验矩阵行和列满足一定约束的规则LDPC码的捕获集结构。几类有限几何和有限域循环和准循环LDPC码与大的最小距离被证明没有有害的陷阱集的大小小于其最小距离。因此，它们的错误平层性能由它们的最小距离决定。
This paper is concerned with construction and structural analysis of both cyclic and quasi-cyclic codes, particularly low-density parity-check (LDPC) codes. It consists of three parts. The first part shows that a cyclic code given by a parity-check matrix in circulant form can be decomposed into descendant cyclic and quasi-cyclic codes of various lengths and rates. Some fundamental structural properties of these descendant codes are developed, including the characterization of the roots of the generator polynomial of a cyclic descendant code. The second part of the paper shows that cyclic and quasi-cyclic descendant LDPC codes can be derived from cyclic finite-geometry LDPC codes using the results developed in the first part of the paper. This enlarges the repertoire of cyclic LDPC codes. The third part of the paper analyzes the trapping set structure of regular LDPC codes whose parity-check matrices satisfy a certain constraint on their rows and columns. Several classes of finite-geometry and finite-field cyclic and quasi-cyclic LDPC codes with large minimum distances are shown to have no harmful trapping sets of size smaller than their minimum distances. Consequently, their error-floor performances are dominated by their minimum distances.