准循环LDPC码不存在四环的充要条件

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 of Quasi-cyclic LDPC Codes without Girth 4

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 according 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 structuring the parity-check matrix. Experimental results indicate that the designed QC-LDPC codes achieve good bit error rate (BER) performance.