扩展原模图LDPC短码的优化构造

Optimal construction of extended short protograph LDPC codes

为设计高纠错性能且低复杂度的准循环-低密度奇偶校验(QC-LDPC)短码,提出了扩展原模图的码优化构造方法.在优化的原模图基础上,通过优化删除节点及扩展该模板校验节点为复合线性分组码扩展节点,并提升子矩阵维度来构造高效短码长QC-LDPC码.采用针对准循环基矩阵渐进边增长(PEG)扩展和准循环-改进的渐进环外消息度(QC-IACE)算法,优化搜索循环置换子矩阵偏移量,联合优化与改善码字停止集、陷阱集及围长与环分布等关系,综合提高码性能.仿真表明:所构造的QC-LDPC短码具有较好的误比特率性能,接近现有高性能随机码字,但码长较短,复杂度和编译码延迟相对较低.

In order to design short quasi-cyclic low-density parity-check（QC-LDPC）codes with good performance and low complexity,an optimization code construction was proposed based on an extension of the protograph.Based on an optimized protograph,an efficient short QC-LDPC code was constructed by properly puncturing and expanding a check nodes in the protograph to a compound block code nodes,followed by enlarging the dimension of the sub-matrices of the code.Thus,ajoint optimization algorithm,combined by the progressive edge growth（PEG）for the optimization of the extended base matrices and the QC improved approximated cycle extrinsic message degree（QC-IACE）for the circulant offset optimizations,was proposed to search the optimal offsets in the circulant permutation sub-matrices of the codeword,which helped to increase code performance by jointly improving and optimizing the stop set and trapping set of the code,as well as girths and cycle profiles.Simulation results indicate that the proposed codes have quite good performance of bit error rate,and compared with current excellent random LDPC code words,the proposed codes obtain almost the same performance.Therefore,the codes can possess low complexity and less latency of encoding and decoding due to their good properties of short code length.