准循环LDPC码不存在四环的充要条件  

The Essential Conditions of Quasi-cyclic LDPC Codes without Girth 4

作　　者：孔令军[1] 赵莹[1] 肖扬[1] 

机构地区：[1]北京交通大学信息科学研究所,北京100044

出　　处：《铁道学报》2009年第6期39-45,共7页Journal of the China Railway Society

基　　金：国家自然科学基金课题(60572093);教育部高等学校博士学科点专项科研基金课题(20050004016)

摘　　要：提出并证明了准循环LDPC码(QC-LDPC码)不存在四环的充要条件,解决了构造任意长度无四环QC-LDPC码的设计问题。根据本文提出的定理调整校验矩阵中循环子矩阵的维数和移位因子,构造无四环的QC-LDPC码。并给出四环检验矩阵方程组,通过确定移位因子及单位子矩阵的阶次,判断四环检验矩阵方程组的值是否全为非零元素,即可确定QC-LDPC码是否无四环。通过成倍增加构造QC-LDPC码无四环所需的最小单位子矩阵阶次,即可获得不同长度无四环的中长码,实现在增加QC-LDPC码码长的同时,确保码字无四环。相比以往常规检验算法,本文的四环检验算法,可缩短运算量,减少检验时间,降低构造校验矩阵的复杂度。计算机仿真结果表明:在有效地消除了四环之后,采用本文所提出定理设计的QC-LDPC码具有良好的BER性能。The essential conditions for quasi-cyclic low-density parity-check codes （QC-LDPC codes） to have no Girth 4 are given. This solves the problem of designing without-girth-4 QC-LDPC codes of any length. Adjusting the dimension and shift factors of the circulant sub-matrices of the given sparse parity-check matrices ac- cording to the proposed theorems, the QC-LDPC codes without girth 4 are constructed. The matrice equation set for girth 4 check is established. Through setting the dimension and shift factors of the circulant sub-matrices, we can check whether the QC-LDPC codes have Girth 4 or not. We can multiply the dimension of the circulant sub-matrices to get the QC-LDPC codes without Girth 4 of different lengths. Our theorems keep the QC- LDPC codes without Girth 4 along with increasing of the code length. Compared to the previous algorithms, the proposed test algorithm decreases computation, shortens the test time and reduces the complexity of struc- turing the parity-check matrix. Experimental results indicate that the designed QC-LDPC codes achieve good bit error rate （BER） performance.

关 键 词：低密度校验码 准循环码 循环矩阵 环 

分 类 号：TN911.2[电子电信—通信与信息系统] TN911.5[电子电信—信息与通信工程]