压缩感知理论在BCH码译码中的应用

(淮北师范大学物理与电子信息学院,安徽 淮北 235000)

压缩感知; 基追踪BP算法; BCH码; 校验矩阵; 伴随式

Research of the BCH Code Decoding Based on the Compressive Sensing Theory
JIANG Enhua,LI Suwen,DOU Dezhao,ZHAO Qingping

(School of Physics and Electronic Information,Huaibei Normal University,Huaibei 235000,China)

compressive sensing; basis pursuit BP algorithm; BCH code; check matrix; syndrome

DOI: 10.6043/j.issn.0438-0479.201702036

备注

借助无噪条件下的压缩感知理论,研究了BCH码的译码方法.将校验矩阵作为测量矩阵,伴随式作为测量信号,建立了重构差错图案的压缩感知模型.采用基追踪BP算法,重构了BCH码的差错图案,以(15,11)BCH码为例,验证了重构的差错图案的正确性.根据收码和差错图案计算出码字估值,通过误码率和码字估值成功率,比较了基追踪BP算法和Berlekamp迭代译码算法的译码效果.以BCH短码和长码为例,进行仿真实验,验证了采用压缩感知理论和基追踪BP算法实现BCH码译码的可行性和有效性.

By means of the compressed sensing theory under no noise condition,this paper conducts a study on the decoding method of the BCH code.The check matrix is used as the measurement matrices,and the syndrome is used as the measurement signal.Hence,the compressed sensing model of the reconstructing error pattern is built.By the basis pursuit BP algorithm,the error pattern of the BCH code is reconstructed.Taking the(15,11)BCH code as an example,we have proved that the reconstructing error pattern is correct.According to the receiving code and the reconstructing error pattern,the value of the code word is calculated.On the basis of bit error rate and the code word estimating success rate,the decoding effect of the basis pursuit BP algorithm and the Berlekamp iterative decoding algorithm are analyzed and compared.Taking the BCH short-code and long-code as an example,the simulation experiment is complete,the experiment results prove that the compressed sensing theory and the basis pursuit BP algorithm are feasible and effective in decoding the BCH code.