基于等差数列与原模图的QC-LDPC码构造方法

针对准循环低密度奇偶校验 (quasi-cyclic low-density parity-check， QC-LDPC)码循环置换矩阵的移位次数确定问题，提出一种基于等差数列与原模图(arithmetic progression and protograph， APP)构造QC-LDPC码的新方法。该方法通过特殊等差算法得出等差数列，原模图结合该等差数列得到待扩展的基矩阵。该方法所构造的QC-LDPC码可灵活地选择码长和码率，而且其校验矩阵的围长至少为8。使用Matlab搭建了通信系统仿真模型，并在此模型基础上基于该构造方法构造的APP-QC-LDPC(4000，2000)码进行了模拟仿真。仿真结果表明，在相同条件下，当误比特率(bit error rate， BER)为10-6时,所构造码率为0.5的APP-QC-LDPC(4000，2000)码相对于基于渐进边增长(progressive edge growth， PEG)算法构造的PEG-QC-LDPC(4000，2000)码、基于等差数列(arithmetic progression， AP)算法构造的AP-QC-LDPC(4000,2000)、基于修饰(masking， M)技术所构造的M-QC-LDPC(4000，2000)码和基于最大公约数(greatest common divisor，GCD)算法所构造的GCD-QC-LDPC(4000，2000)码分别能改善约0.46，0.55，0.9和1.06 dB的净编码增益(net coding gain， NCG)，具有较好的纠错性能。

Construction method of QC-LDPC codes based on the arithmetic progression and protograph

A new construction method of QC-LDPC codes based on the arithmetic progression and protograph(APP) is proposed in order to solve the problem of determining shift times of the circulant permutation matrix(CPM) in quasi-cyclic low-density parity-check(QC-LDPC) codes. The base matrix expanded is obtained by combining the protograph with the arithmetic progression which is obtained by the special arithmetic algorithm. The code length and code rate of the QC-LDPC codes constructed by this method can be adjusted flexibly, and the QC-LDPC codes have the check matrix with girth-8 at least. The simulation model of communication system is established by Matlab program. And based on the model, the APP-QC-LDPC(4 000,2 000) code constructed by the proposed construction method is emulated and analyzed. The simulation results reflect that at the bit error rate (BER) of 10-6, the net coding gain of the APP-QC-LDPC(4 000,2 000) code is respectively 0.46 dB, 0.55 dB, 0.9 dB and 1.06 dB more than those of the PEG-QC-LDPC (4 000,2 000) code based on progressive edge growth (PEG) algorithm, the AP-QC-LDPC(4 000,2 000) code based on the arithmetic progression, the M-QC-LDPC (4 000,2 000) code based on masking(M) technology and the GCD-QC-LDPC (4 000,2 000) code based on greatest common divisor(GCD) algorithm at the same condition, which has the better error-correction performance.