基于压缩感知理论的汉明码译码

Compressed sensing based decoding of Hamming code

借助压缩感知理论研究汉明码译码问题,并将求解差错图案的问题转化为线性规划问题。借助无噪声干扰条件下的压缩感知观测模型,推导出差错图案重构的压缩感知模型。采用基追踪算法,把伴随式作为测量信号,校验矩阵作为测量矩阵,以(15,11)汉明码为例,完成对差错图案的重构,并验证其正确性。根据收码和重构差错图案计算出码字估值。从误码率和码字估值成功率两方面,比较硬判决译码算法、最大似然译码算法和基追踪算法的译码效果。仿真实验结果显示,采用无噪条件下的压缩感知理论和基追踪算法的汉明码译码可行且有效。

The compressed sensing theory can be used for decoding of Hamming code, and the error pattern problem can be transformed into a linear programming problem. Based on the compressed sensing model under the condition of no noise interference, the compressed sensing model of error pattern reconstruction is derived. By using the basis pursuit algorithm, taking the syndrome as the measurement signal, the check matrix as the measurement matrix, and Hamming code （15, 11） as an example, the error pattern is reconstructed and verified to be correct. The codeword value is calculated according to the received code and the reconstructing error pattern. From the two aspects of bit error rate and codeword estimating success rate, the decoding effect of the basis pursuit algorithm is analyzed, and compared with the hard decision decoding algorithm and the maximum likelihood decoding algorithm. The simulation results show that the decoding method for Hamming code based on the basis pursuit algorithm and the compressed sensing theory under the condition of no noise is feasible and effective.