中文标题#
刪除 / 替代信道容量的表徵對於小的刪除和替代概率
英文标题#
Characterization of Deletion/Substitution Channel Capacity for Small Deletion and Substitution Probabilities
中文摘要#
我們考慮二進制輸入刪除 / 替換信道，這模擬了實際中遇到的某些同步錯誤類型。 具體來說，我們關注刪除和替換概率較小的區域，並通過擴展針對僅刪除信道開發的方法，得到了獨立同分布（i.i.d.）刪除 / 替換信道的漸近信道容量表徵。 為此，給定一個成功的解碼概率，我們首先為固定數量的刪除和替換開發了一個碼本大小的上界，然後將結果擴展到隨機刪除和替換的情況，以得到信道容量的上界。 我們的最終結果是： 獨立同分布的刪除 / 替換信道容量大約為 (1 - H (p_d) - H (p_s))，對於 (p_d, p_s \approx0)，其中 (p_d) 和 (p_s) 分別是刪除和替換的概率。
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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