We consider binary input deletion/substitution channels, which model certain channels with synchronization errors encountered in practice. Specifically, we focus on the regime of small deletion and substitution probabilities, and by extending an approach developed for the deletion-only channel, we obtain an asymptotic characterization of the channel capacity for independent and identically distributed deletion/substitution channels. We first present an upper bound on the capacity for arbitrary but fixed numbers of deletions and substitutions, and then we extend the result to the case of random deletions and substitutions. Our final result is as follows: The i.i.d. deletion/substitution channel capacity is approximately $1 - H(p_d) - H(p_s)$, for $p_d, p_s \approx0$, where $p_d$ is the deletion probability, and $p_s$ is the substitution probability.

翻译：本文研究二进制输入删除/替换信道，该模型可刻画实际中遇到的具有同步误差的特定信道。我们重点考察小概率删除与替换场景，通过扩展针对纯删除信道所建立的方法，获得了独立同分布删除/替换信道容量的渐近刻画。首先给出任意固定数量删除与替换情况下的容量上界，随后将结果推广至随机删除与替换的情形。最终结论表明：当删除概率$p_d$与替换概率$p_s$趋近于零时，独立同分布删除/替换信道的容量近似为$1 - H(p_d) - H(p_s)$，其中$p_d$为删除概率，$p_s$为替换概率。