Unique Reconstruction of Coded Strings from Multiset Substring Spectra

一种从子串组合重构字符串的新代数方法

A New Algebraic Approach for String Reconstruction from Substring Compositions

针对子串组合多重集下的二进制字符串重构问题，提出基于二元多项式代数性质的新算法，在特定条件下免回溯，将复杂度降至 O(n^2) 并构造更大重构码。

Multi-strand Reconstruction from Substrings

The problem of string reconstruction based on its substrings spectrum has received significant attention recently due to its applicability to DNA data storage and sequencing. In contrast to previous works, we consider in this paper a setup of this problem where multiple strings are reconstructed together. Given a multiset $S$ of strings, all their substrings of some fixed length $\ell$, defined as the $\ell$-profile of $S$, are received and the goal is to reconstruct all strings in $S$. A multi-strand $\ell$-reconstruction code is a set of multisets such that every element $S$ can be reconstru…

Reconstruction of a Single String from a Part of its Composition Multiset

Motivated by applications in polymer-based data storage, we study the problem of reconstructing a string from part of its composition multiset. We give a full description of the structure of the strings that cannot be uniquely reconstructed (up to reversal) from their multiset of all of their prefix-suffix compositions. Leveraging this description, we prove that for all $n\ge 6$, there exists a string of length $n$ that cannot be uniquely reconstructed up to reversal. Moreover, for all $n\ge 6$, we explicitly construct the set consisting of all length $n$ strings that can be uniquely reconstru…

论噪声子串信道的编码

On Codes for the Noisy Substring Channel

研究噪声子串信道的编码问题，针对替换和删除噪声提出纠错码族及组合界，证明次线性冗余且无渐近速率损失，并开发高效编码器以避免DNA链二级结构形成。

从含噪子串进行重构

Reconstruction from Noisy Substrings

针对 DNA 存储中由带最小重叠的含噪连续子串唯一恢复序列的问题，本文研究单链与多链重构码，构造新码并使部分速率渐近达到上界。

String Reconstruction from Substring Compositions

Motivated by mass-spectrometry protein sequencing, we consider a simply-stated problem of reconstructing a string from the multiset of its substring compositions. We show that all strings of length 7, one less than a prime, or one less than twice a prime, can be reconstructed uniquely up to reversal. For all other lengths we show that reconstruction is not always possible and provide sometimes-tight bounds on the largest number of strings with given substring compositions. The lower bounds are derived by combinatorial arguments and the upper bounds by algebraic considerations that precisely ch…