基于环路分类的围长至少为10的QC-LDPC码显式构造方法  

Explicit construction of QC-LDPC codes with girth at least ten based on cycle classification

作　　者：谷静 范裕子 张国华[2,3] Gu Jing;Fan Yuzi;Zhang Guohua(School of Electronic Engineering,Xi an University of Posts&Telecommunications,Xi an 710121,China;Xi an Branch,China Academy of Space Technology,Xi an 710100,China;Institute for Theoretical Information Technology,RWTH Aachen University,Aachen 52074,Germany)

机构地区：[1]西安邮电大学电子工程学院,西安710121 [2]中国空间技术研究院西安分院,西安710100 [3]德国亚琛工业大学理论信息技术研究所,德国亚琛52074

出　　处：《计算机应用研究》2018年第1期204-207,共4页Application Research of Computers

基　　金：国家自然科学基金资助项目(61471294);陕西省教育厅科学研究项目计划资助项目(15JK1654)

摘　　要：对于围长至少为10的(3,L)-规则准循环(QC)低密度奇偶校验(LDPC)码,现有的显式构造法在参数选取上不够灵活。针对该问题,提出一种基于环路分类的显式构造方法。该方法在构造过程中,首先在循环置换矩阵(CPM)尺寸为无穷大的假设下,考虑各种长度小于10的环路形状导致的等式约束,以渐进方式确定出QC-LDPC码对应的指数矩阵中的每个元素的取值下界;然后根据指数矩阵确定出CPM尺寸的连续取值下界。这种方法允许L任意取值,允许CPM尺寸在一个门限以上任意取值。仿真结果表明,对于L=5,新码与Tanner提出的围长为12的(3,5)-规则QC-LDPC码的译码性能几乎一致。For the construction of(3,L)-regular quasi-cyclic(QC)low-density parity-check codes with girth at least ten,the existing explicit methods are not flexible in the selection of parameters.As to this problem,this paper proposed a novel explicit method on the basis of cycle classification.In the construction procedure,it considered all equation constraints governing all cycles with lengths smaller than ten for the case of an infinite circulant-permutation-matrix(CPM)size.Then,it determined all elements within an exponent matrix for a QC-LDPC code as lower bounded progressively.Finally,it determined a lower bound above which CPM size could vary consecutively based on the entries within the exponent matrix.The new approach enables both an arbitrary L and an arbitrary CPM size above a certain lower bound.Simulation results show that,for L=5,the new codes perform as well as Tanner’s(3,5)-regular QC-LDPC codes with girth 12.

关 键 词：低密度奇偶校验码 准循环 围长 循环置换矩阵 指数矩阵 显式构造 

分 类 号：TN911.22[电子电信—通信与信息系统]