Marker+Codeword+Marker：一种用于分段单插入删除/编辑信道的编码结构
Marker+Codeword+Marker: A Coding Structure for Segmented Single-Insdel/-Edit Channels
AI总结：
本文针对分段边界未知的单插入删除/编辑信道，提出标记+码字+标记编码结构并结合VT码，首次构造出具有线性时间编解码器且冗余度分别为$\log_2(n-6)+7$和$\log_2(n-9)+10$比特的二进制纠错码。
摘要：
插入删除（insdel）指一次删除或一次插入，编辑（edit）指一次插入删除或一次替换。本文考虑分段单插入删除（相应地，单编辑）信道，其中信道的输入比特流被划分为长度为$n$的段，每段至多遭受一次单插入删除（相应地，单编辑）错误。$n$的值对接收端已知，但段的边界未知。我们提出按照“标记+码字+标记”的结构对每一段进行编码，其中两个标记经过精心选择，码字取自Varshamov-Tenegolts（VT）码。通过这种方式，我们能够构造出一类新的二进制码，可以纠正分段单插入删除错误。我们的码具有最低冗余度$\log_2(n-6)+7$比特，并且是文献中第一个具有线性时间编码器/解码器的码。此外，通过增强VT码和其中一个标记，我们能够构造出第一类可以纠正分段单编辑错误的二进制码。这类码的冗余度为$\log_2(n-9)+10$比特，并且具有线性时间编码器/解码器。
英文摘要：
An insdel refers to a deletion or an insertion, and an edit refers to an insdel or a substitution. In this paper, we consider the segmented single-insdel (resp. single-edit) channel, where the channel's input bit stream is partitioned into segments of length $n$ and each segment can suffer from at most a single insdel (resp. edit) error. The value of $n$ is known to the receiver but the boundaries of segments are not. We propose to encode each segment following a marker+codeword+marker structure, where the two markers are carefully selected and the codewords are chosen from Varshamov-Tenegolts (VT) codes. In this way, we are able to construct a new class of binary codes that can correct segmented single-insdel errors. Our codes have the lowest redundancy of $\log_2(n-6)+7$ bits and are the first one that has linear-time encoder/decoder in the literature. Moreover, by enhancing the VT codes and one of the markers, we are able to construct the first class of binary codes that can correct segmented single-edit errors. This class of codes has redundancy $\log_2(n-9)+10$ bits and has linear-time encoder/decoder.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
