Conditional Entropies of k-Deletion/Insertion Channels

IF 2.9 3区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Information Theory Pub Date : 2025-06-23 DOI:10.1109/TIT.2025.3581849

Shubhransh Singhvi;Omer Sabary;Daniella Bar-Lev;Eitan Yaakobi

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引用次数: 0

Abstract

The channel output entropy of a transmitted sequence is the entropy of the possible channel outputs, and similarly, the channel input entropy of a received sequence is the entropy of all possible transmitted sequences. The goal of this work is to study these entropy values for the k-deletion and k-insertion channels, where exactly k symbols are deleted or inserted in the transmitted sequence, respectively. If all possible sequences are transmitted with the same probability, then studying the input and output entropies becomes equivalent. For both the 1-deletion and 1-insertion channels, it is shown that among all sequences with a fixed number of runs, the input entropy is minimized for sequences with a skewed distribution of run lengths, and it is maximized for sequences with a balanced distribution of run lengths. Among our results, we establish a conjecture by Atashpendar et al., which claims that for the 1-deletion channel, the input entropy is maximized by the alternating sequences among all binary sequences. This conjecture is also verified for the 2-deletion channel, where it is proved that sequences with a single run minimize the input entropy.

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k-删除/插入通道的条件熵

传输序列的信道输出熵是可能的信道输出熵，同样，接收序列的信道输入熵是所有可能的传输序列的熵。这项工作的目标是研究k-删除和k-插入通道的熵值，其中在传输序列中分别删除或插入k个符号。如果所有可能的序列都以相同的概率传输，那么研究输入和输出熵就等价了。对于1-删除和1-插入通道，结果表明，在所有固定运行数的序列中，对于运行长度分布偏斜的序列，输入熵最小，对于运行长度分布平衡的序列，输入熵最大。在我们的研究结果中，我们建立了Atashpendar等人的一个猜想，该猜想声称对于1删除信道，所有二进制序列之间的交替序列使输入熵最大化。这个猜想也在2删除通道中得到了验证，其中证明了单次运行的序列使输入熵最小化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IEEE Transactions on Information Theory 工程技术-工程：电子与电气

CiteScore

5.70

自引率

20.00%

发文量

514

审稿时长

12 months

期刊介绍： The IEEE Transactions on Information Theory is a journal that publishes theoretical and experimental papers concerned with the transmission, processing, and utilization of information. The boundaries of acceptable subject matter are intentionally not sharply delimited. Rather, it is hoped that as the focus of research activity changes, a flexible policy will permit this Transactions to follow suit. Current appropriate topics are best reflected by recent Tables of Contents; they are summarized in the titles of editorial areas that appear on the inside front cover.