中文标题#
删除 / 替代信道容量的表征对于小的删除和替代概率
英文标题#
Characterization of Deletion/Substitution Channel Capacity for Small Deletion and Substitution Probabilities
中文摘要#
我们考虑二进制输入删除 / 替换信道，这模拟了实际中遇到的某些同步错误类型。 具体来说，我们关注删除和替换概率较小的区域，并通过扩展针对仅删除信道开发的方法，得到了独立同分布（i.i.d.）删除 / 替换信道的渐近信道容量表征。 为此，给定一个成功的解码概率，我们首先为固定数量的删除和替换开发了一个码本大小的上界，然后将结果扩展到随机删除和替换的情况，以得到信道容量的上界。 我们的最终结果是： 独立同分布的删除 / 替换信道容量大约为 (1 - H (p_d) - H (p_s))，对于 (p_d, p_s \approx0)，其中 (p_d) 和 (p_s) 分别是删除和替换的概率。
英文摘要#
We consider binary input deletion/substitution channels, which model certain types of 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 (i.i.d.) deletion/substitution channels. To do so, given a target probability of successful decoding, we first develop an upper bound on the codebook size for arbitrary but fixed numbers of deletions and substitutions, and then extend the result to the case of random deletions and substitutions to obtain a bound on the channel capacity. Our final result is: 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) and (p_s) are the deletion and substitution probabilities, respectively.
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