基于偏移量周期填充的 QC-LDPC 码构造方法

准循环低密度奇偶校验卷积 (QC-LDPC-C: Quasi-Cyclic Low Density Parity-Check Convolutional)码其校验 矩阵的构造需避免 4 环，且不考虑结构特点的直接构造会使构造的计算复杂度呈指数增长。为此，提出 QC-LDPC-C码的基于子矩阵偏移量周期性填充的构造方法。该方法利用基校验矩阵的周期性，首先填充基校 验矩阵中确定的子矩阵部分，以实现快速编码，而后在基校验矩阵的随机子矩阵的构造中采用子矩阵偏移量的 优化选择，使每次位置选择并周期性填充后获得的矩阵能满足无 4 环的扩展矩阵结构，得到扩展后无4 环的基 校验矩阵，从而令扩展后的校验矩阵的围长至少为 6。将具有不同参数的 LDPC-C 码与基于该方法构造的 QC-LDPC-C码进行测试和比较，实验结果表明，后者可获得较好的译码性能，同时编译码复杂度较低。

Research of Spectrum Sensing in Cognitive Radio Network

The construction of parity check matrices for QC-LDPC-C (Quasi-Cyclic Low Density Parity-Check Convolutional) codes needs to be free of length-4 cycles，and the computational complexity of direct construction will increase exponentially without considering the characteristics of matrices． The construction for QC-LDPC-C codes based on periodic filling with offsets of sub-matrices is proposed． With the periodicity of the base check matrix，the proposed method fills the deterministic sub-matrices to realize fast encoding; during the construction for random sub-matrices，the optimized selection with offsets of sub-matrices is utilized to ensure that the obtained matrix after each selection for sub-matrix position and periodic expansion satisfies the expended structure without length-4 cycles． The base check matrix whose expanded matrix is free of length-4 cycles can be obtained，and the girth of expanded check matrix is at least 6． LDPC-C codes with different parameters are used to compare with the constructed QC-LDPC-C codes． Experimental results show that the codes constructed with proposed method can achieve better performance and lower encoding and decoding complexity．