AWGN信道下线性分组码的差错概率下界分析

提出了一种线性分组码的最大似然译码(ML-decoding)差错概率下界的计算方法。差错概率的下界优化实质上是对联合事件概率下界的优化,算法结合改进的Dawson-Sankoff界的优化准则,提出了AWGN信道下线性分组码差错冗余事件的判决准则,得到了误码率下界的计算表达式。该表达式只依赖码字的Hamming重量分布与信噪比,较之类deCaens界与类KAT界,本算法得到的下界更紧,计算量更低。针对LDPC等线性分组码的数值结果证明了算法的优越性能。

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

A lower bound on the error rate of linear binary block codes (under maximum likelihood decoding) over BPSK-modulated AWGN channels is proposed in the current study. The essence of the optimization to the lower error rate bound is to optimize the lower bound on the union probability of finite events. Combined with the optimizing rule of the improved Dawson-sankoff bound, we obtain the judge rule of the redundant error events and obtain the calculation expression about lower bound of SER which solely depends on the Hamming weight enumerator function of the code and the signal-to-noise ratio (Eb/N0). The algorithm can get the tighter lower bound and has lower complexity than the de Caen's kind bound and the KAT kind bound, which has been proved by the numerical results applying to LDPC codes and the others.