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）上采用非均匀输入分布传输分组码，并通过最大后验概率（MAP）解码规则进行解码时的错误概率。证明了MAP解码器连通分量的概率与无MAP解码连通分量时错误概率之比至多随码块长度线性增长，从而表明解码连通分量不会影响码的错误指数。该结果推广了近期关于在BSC上以均匀输入分布传输分组码的类似结论。