基于BP算法的线性分组码译码研究  

Research of the linear block codes decoding based on the basis pursuit BP algorithm

作　　者：姜恩华[1] 窦德召[1] 赵庆平[1] 

机构地区：[1]淮北师范大学物理与电子信息学院,安徽淮北235000

出　　处：《云南大学学报（自然科学版）》2018年第1期36-42,共7页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(41475017;11504121);安徽省高校自然科学研究重点项目(KJ2016A628;KJ2016A650)

摘　　要：在压缩感知理论中,基追踪BP算法用于求解l1范数的最小值问题,采用原对偶内点法实现对稀疏信号的重构.在线性分组码译码中,把差错图案E看作一维稀疏信号,借助压缩感知理论,提出了重构差错图案E的方法.把伴随式S和校验矩阵H分别作为测量信号和测量矩阵,代入基追踪BP算法重构出差错图案E.验证了重构的差错图案E是正确的.对线性分组码译码进行仿真实验,通过基追踪BP算法和最大似然算法实现了汉明码的译码,通过基追踪BP算法和Berlekamp算法实现了BCH码的译码.通过比较译码的误码率BER和码字C估值的成功率,可以看出,采用压缩感知理论和基追踪BP算法较好地实现了对汉明码和BCH码的译码.In the compressed sensing theory, the Basis Pursuit BP algorithm can solve the problem of the minimum value of the 11 norm.The Primal-dual interior point method is used to reconstruct the sparse signal.For the linear block code decoding,if the error pattern E is treated as the one-dimensional sparse signal, the compressed sensing model of the reconstructing error pattern E is deduced by the compressed sensing under the no noise condition.The check matrix H is used as the measurement matrix, and the syndrome S is used as the meas- urement signal.The error pattern E can be reconstructed by the Basis Pursuit BP algorithm.It proves that the re- constructing error pattern E is correct.The simulation experiment of decoding the linear block code is designed. The Hamming code is decoded by the basis pursuit BP algorithm and the maximum likelihood algorithm.The BCH code is decoded by the basis pursuit BP algorithm and the Berlekamp algorithm.By the bit error rate and the code word C reconstructing success rate, the decoding performance is compared and analyzed.The simulation experiment result proves that the hamming code and the BCH code can be decoded well by the compressed sensing theory and the basis pursuit BP algorithm.

关 键 词：基追踪BP算法 汉明码 BCH码 压缩感知 差错图案 伴随式 

分 类 号：TN911.7[电子电信—通信与信息系统]