多信源多中继编码协作系统准循环LDPC码的联合设计与性能分析

Joint Design of Quasi-cyclic Low Density Parity Check Codes and Performance Analysis of Multi-source Multi-relay Coded Cooperative System

为解决多信源多中继低密度奇偶校验(LDPC)码编码协作系统编码复杂度高、编码时延长的问题,该文引入一种特殊结构的LDPC码基于生成矩阵的准循环LDPC码(QC-LDPC)码。该类码结合了QC-LDPC码与基于生成矩阵LDPC(G-LDPC)码的特点,可直接实现完全并行编码,极大地降低了中继节点的编码时延及编码复杂度。在此基础上,推导出对应于信源节点和中继节点采用的QC-LDPC码的联合校验矩阵,并基于最大公约数(GCD)定理联合设计该矩阵以消除其所有围长为4,6(girth-4,girth-6)的短环。理论分析和仿真结果表明,在同等条件下该系统的误码率(BER)性能优于相应的点对点系统。仿真结果还表明,与采用显式算法构造QC-LDPC码或一般构造QC-LDPC码的协作系统相比,采用联合设计QC-LDPC码的系统均可获得更高的编码增益。

To solve the problems of high encoding complexity and long encoding delay in the multi-source multi-relay Low Density Parity Check(LDPC)coded cooperative system,a special kind of structured LDPC codes Quasi-Cyclic LDPC(QC-LDPC)codes based on generator matrix is proposed,which combines the characteristics of QC-LDPC codes and Generator-matrix-based LDPC(G-LDPC)codes.It can perform completely parallel encoding,which greatly reduces the encoding complexity and delay at the relays.Based on this,a joint parity check matrix corresponding to the QC-LDPC codes adopted by the sources and relays is deduced,and the matrix is further jointly designed based on the Greatest Common Divisor(GCD)theorem to eliminate all cycles of girth-4 and girth-6.Theoretical analysis and simulation results show that under the same conditions,the Bit Error Rate(BER)performance of the proposed system is better than that of the corresponding point-to-point system.The simulation results also show that the cooperative system with jointly designed QC-LDPC codes can obtain a higher coding gain than the system with explicitly constructed QC-LDPC codes or generally constructed QC-LDPC codes.