一种基于环路分类和启发式搜索的大围长QC-LDPC码构造新方法  

New Construction of Large-girth QC-LDPC Codes by Classification of Cycles and Heuristic Search Strategy

作　　者：张国华[1] 张建华[1] 

机构地区：[1]中国空间技术研究院西安分院,西安710000

出　　处：《空间电子技术》2013年第2期79-84,89,共7页Space Electronic Technology

摘　　要：文章通过对QC-LDPC码校验矩阵中的环路进行分类,提出一种检测所有长度小于12的环的无重无漏方法。利用该环路检测方法,提出了一种新的基于启发搜索的大围长QC-LDPC码构造法。该构造法分3步:首先,在无穷大CPM尺寸条件下根据启发策略搜索2条满足围长约束的整数序列;然后,依据设计码率从2条序列中截取若干整数对构成一个移位矩阵;最后,利用最近Zhang提出的理论下界从该移位矩阵中精确计算出使围长不减的CPM尺寸连续取值区间。与Liu-Han方法相比,新方法有2个优点:(1)既可以构造CPM尺寸连续变化的girth-10+QC-LDPC码,也可以构造CPM尺寸连续变化的girth-12 QC-LDPC码;(2)由于新环路检测方法有效提高了序列搜索速度,因此可以构造出设计码率非常高的girth-10+和girth-12 QC-LDPC码。By classifying cycle types within the parity-check matrix of a quasi-cyclic （QC） low-density parity-check （LDPC） code, a method without repetition or omission is proposed to detect all the cycles with lengths smaller than twelve. Based on this cycle detection method, a new approach is presented to construct large girth QC-LDPC codes by using some heuristic strategies. The approach includes three steps. Firstly, under the infinite cyclic permutation matrix （CPM） size con- dition, two integer sequences satisfying the girth constraint are found using a heuristic strategy. Secondly, according to the de- signed code rate, several integer pairs are extracted from the two sequences so as to form a shift matrix. Finally, by employing the recently proposed theoretical lower bound by Zhang et. al, a range of consecutive CPM sizes in which the girth never de- crease is accurately computed from the shift matrix. Compared with Liu-Han＇s method, the new approach possesses two ad- vantages in the sense that： （1） Not only girth-10 ＋ QC-LDPC codes but also girth-12 ones can be constructed to have consecutive CPM sizes;（2） girth-10 ＋ and girth-12 QC-LDPC codes can be generated with very high code rates, due to the new cycle detection method which significantly accelerates the sequence search procedure.

关 键 词：低密度奇偶校验码 准循环 环 围长 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]