The error probability of block codes sent under a non-uniform input distribution over the memoryless binary symmetric channel (BSC) and decoded via the maximum a posteriori (MAP) decoding rule is investigated. It is proved that the ratio of the probability of MAP decoder ties to the probability of error when no MAP decoding ties occur grows at most linearly in blocklength, thus showing that decoder ties do not affect the code's error exponent. This result generalizes a similar recent result shown for the case of block codes transmitted over the BSC under a uniform input distribution.

翻译：本文研究了在无记忆二元对称信道（BSC）上以非均匀输入分布传输的块码，并采用最大后验（MAP）译码规则进行译码时的错误概率。证明了MAP译码器平局概率与无平局时错误概率之比随码长至少线性增长，从而表明译码器平局不影响码的错误指数。这一结果推广了近期关于均匀输入分布下BSC传输块码情形的类似结论。