In the sequence reconstruction problem, a codeword $\x$ is transmitted through several identical channels where each channel produces a noisy read of $\x$, and the problem is to analyze how to uniquely reconstruct $\x$ based on these noisy reads. Levenshtein has studied the minimum number of reads which guarantees unique reconstruction of $\x$, which is one sufficient condition for unique reconstruction. In this paper, we move on to a different perspective and propose a new framework for unique reconstruction. Our new sufficient condition for unique reconstruction takes both the number of reads and the distances among the reads into consideration. We offer both theoretical analysis and corresponding efficient reconstruction algorithms for our reconstruction framework.

翻译：在序列重建问题中，码字 $\x$ 通过若干相同信道传输，每个信道产生 $\x$ 的一个含噪读取结果，问题在于分析如何基于这些含噪读取结果唯一地重建 $\x$。Levenshtein 研究了保证 $\x$ 唯一重建所需的最小读取次数，这是唯一重建的一个充分条件。本文另辟蹊径，提出了一种新的唯一重建框架。我们提出的新充分条件同时考虑了读取次数及读取结果之间的差异。针对这一重建框架，我们既进行了理论分析，又给出了相应的有效重建算法。