基于gOMP算法的循环码译码研究

在压缩感知理论中,广义正交匹配追踪(gOMP)算法常用于解决l0范数的最小化问题.借助无噪声干扰的压缩感知观测模型,提出了循环码差错图案E重构的压缩感知模型,以校验矩阵H作为测量矩阵,伴随式S作为测量信号,采用gOMP算法重构了差错图案E,其与收码R进行模2加运算,求得发码C的估值.进一步提出了校验矩阵H作为测量矩阵的构成形式及其2个定理.详细论述了gOMP算法重构差错图案E的计算过程.以(7,1)、(7,3)、(7,4)、(15,7)和(31,21)循环码为例,分析了gOMP算法对循环码的纠错能力;以(7,1)循环码为例,分析了gOMP算法中原子选取个数s与纠错位数的关系.通过误码率和码字C重构的成功率,比较分析了gOMP算法和最大似然译码算法的译码效果.仿真实验表明,采用压缩感知理论和广义正交匹配追踪gOMP算法实现循环码译码是可行和有效的.

Research on the cyclic codes decoding based on the generalized orthogonal matching pursuit gOMP algorithm

The generalized orthogonal matching pursuit gOMP algorithm has been used in the compressed sensing theory to solve the minimizing problem of the l₀ norm. According to the compressed sensing model under the no noise condition, the compressed sensing model of the reconstructing error pattern E of the cyclic code is built in this paper. With the check matrix H as the measurement matrix, the syndrome S as the measurement signal, the error pattern E is reconstructed using the gOMP algorithm, while the value of the code word C is calculated by the receiving code R adding the error pattern E on modulo 2. Furthermore, we provide the form of the check matrix H, and propose two relevant theorems. The error correction ability of the gOMP algorithm is analyzed through some cyclic code examples, and the relationship between the selecting atom number s of the gOMP algorithm and the error correction bits is investigated. Finally, based on the bit error rate and the code word C reconstructing success rate, the decoding effects of the gOMP algorithm and the maximum likelihood algorithm are analyzed and compared. The simulation experiment results prove that the compressed sensing theory and gOMP algorithm are feasible and effective in decoding the cyclic code.