The sequence reconstruction problem for insertion/deletion channels has attracted significant attention owing to their applications recently in some emerging data storage systems, such as racetrack memories, DNA-based data storage. Our goal is to investigate the reconstruction problem for sticky-insdel channels where both sticky-insertions and sticky-deletions occur. If there are only sticky-insertion errors, the reconstruction problem for sticky-insertion channel is a special case of the reconstruction problem for tandem-duplication channel which has been well-studied. In this work, we consider the $(t, s)$-sticky-insdel channel where there are at most $t$ sticky-insertion errors and $s$ sticky-deletion errors when we transmit a message through the channel. For the reconstruction problem, we are interested in the minimum number of distinct outputs from these channels that are needed to uniquely recover the transmitted vector. We first provide a recursive formula to determine the minimum number of distinct outputs required. Next, we provide an efficient algorithm to reconstruct the transmitted vector from erroneous sequences.

翻译：序列重构问题在插入/删除信道中因近期在赛道存储器、基于DNA的数据存储等新兴数据存储系统中的应用而受到广泛关注。本文旨在研究同时存在粘性插入与粘性删除错误的粘性插入删除信道中的重构问题。若仅存在粘性插入错误，则粘性插入信道的重构问题是已被充分研究的串联复制信道重构问题的一个特例。本研究考虑$(t,s)$-粘性插入删除信道：当消息通过该信道传输时，最多发生$t$次粘性插入错误和$s$次粘性删除错误。针对重构问题，我们关注唯一恢复传输向量所需这些信道输出的最小不同数目。首先给出确定所需最小不同数目的递归公式，进而提出一种从错误序列中重构传输向量的高效算法。