论文标题
$ k $ deToption/插入频道的输入和输出熵
The Input and Output Entropies of the $k$-Deletion/Insertion Channel
论文作者
论文摘要
传输单词的通道输出熵是可能的通道输出的熵，同样，接收的单词的输入熵是所有可能的传输单词的熵。这项工作的目的是研究K-Deotion，K插入通道的这些熵值，其中k插入通道准确地删除了k符号并分别插入传输单词。如果所有可能的单词都以相同的概率传输，那么研究输入和输出熵是等效的。对于1个插入和1局部通道，证明在所有固定数量运行的单词中，对于单词，输入熵的单词被偏向于其运行长度的分布，并且具有平衡的运行长度分布的单词最大化。在我们的结果中，我们建立了Atashpendar等人的猜想。这声称对于二进制1删除，对于交替单词，输入熵最大化。该猜想也已被验证为2台式通道，在该通道中可以证明，单个运行的常数单词最小化输入熵。
The channel output entropy of a transmitted word is the entropy of the possible channel outputs and similarly, the input entropy of a received word is the entropy of all possible transmitted words. The goal of this work is to study these entropy values for the k-deletion, k-insertion channel, where exactly k symbols are deleted, and inserted in the transmitted word, respectively. If all possible words are transmitted with the same probability then studying the input and output entropies is equivalent. For both the 1-insertion and 1-deletion channels, it is proved that among all words with a fixed number of runs, the input entropy is minimized for words with a skewed distribution of their run lengths and it is maximized for words with a balanced distribution of their run lengths. Among our results, we establish a conjecture by Atashpendar et al. which claims that for the binary 1-deletion, the input entropy is maximized for the alternating words. This conjecture is also verified for the 2-deletion channel, where it is proved that constant words with a single run minimize the input entropy.
