BSC信道下线性分组码的差错概率下界分析

Analysis of Lower Bound for the Error Probability of Linear Block Codes over the BSC Channel

针对BSC信道,提出了一种线性分组码的最大似然译码差错概率下界的计算方法。根据最大似然译码算法原理,首先将译码差错概率转化为差错事件的联合概率,基于改进的Dawson-Sankoff界的优化准则,推导出BSC信道下线性分组码差错冗余事件的判决准则,最后得到差错概率下界的计算表达式。该下界只依赖于码字的Hamming重量分布与信道的交叉概率。针对不同的LDPC码的仿真结果表明:较之常见的下界和sphere packing bound,本算法得到的下界性能更好、计算复杂度更低。

A lower bound on the error rate of linear binary block codes （under maximum likelihood decoding） over BSC channels is proposed. According to the principle of the maximum likelihood （ML） decoding algorithm, the decoding error probability is firstly converted into the joint probability of the error events, and the judge rule of the redundant error events is deduced based on the optimization rule of the improved Dawson-Sankoff bound. Moreover, the calculation expression about lower bound of the error probability solely depends on the Hamming weight enumerator function of the code and the crossover probability of the channel. The simulation results applying to various LDPC codes show that the new lower bound outperforms those genetic lower bounds and the sphere packing bound. Its computational complexity is also lower.