Reconstruction from Substrings with Partial Overlap

TL;DR

This paper develops a new class of reconstruction codes for DNA data storage, focusing on reading overlapping substrings, providing bounds and optimal constructions for reliable sequence reconstruction.

Contribution

It introduces a novel family of codes for reconstructing sequences from overlapping substrings, extending previous models and achieving asymptotic optimality.

Findings

Derived upper bounds on code rates for unique reconstruction

Constructed asymptotically optimal codes meeting these bounds

Enhanced understanding of reconstruction from overlapping substrings

Abstract

This paper introduces a new family of reconstruction codes which is motivated by applications in DNA data storage and sequencing. In such applications, DNA strands are sequenced by reading some subset of their substrings. While previous works considered two extreme cases in which \emph{all} substrings of some fixed length are read or substrings are read with no overlap, this work considers the setup in which consecutive substrings are read with some given minimum overlap. First, upper bounds are provided on the attainable rates of codes that guarantee unique reconstruction. Then, we present efficient constructions of asymptotically optimal codes that meet the upper bound.