This manuscript investigates channel capacity under mismatched stochastic likelihood decoding. We derive Feinstein- and Verdú-Han-style bounds on the error probability coded communication. These are used to obtain a general information-spectrum formula for the channel capacity under mismatched stochastic decoding. The mismatch capacity formula is expressed as the supremum over all input distribution sequences of the limit inferior in probability of the sequence of normalized mismatched information densities. The resulting capacity formula is the mismatched analog of the channel capacity formula for the matched case by Verdú and Han. We also show that when the sequence of normalized mismatched information densities is uniformly integrable, the capacity formula admits an upper-bound as the limit of the corresponding sequence of expectations. This upper-bound is shown to be achievable for discrete-memoryless channels and product decoding metrics, showing that the Csiszár-Narayan conjecture is tight for mismatched stochastic decoders.

翻译：本文研究了错配随机似然解码下的信道容量。我们推导了编码通信错误概率的Feinstein型和Verdú-Han型界，并利用这些界获得了错配随机解码下信道容量的一般信息谱公式。该错配容量公式表示为所有输入分布序列上概率意义下的归一化错配信息密度序列的下极限的上确界。所得容量公式是Verdú与Han在匹配情形下信道容量公式的错配版本。我们还证明，当归一化错配信息密度序列满足一致可积性时，容量公式存在一个上界，即相应期望序列的极限。这一上界对离散无记忆信道和乘积解码度量是可达的，表明Csiszár-Narayan猜想对于错配随机解码器是紧致的。