Codes for DNA Storage Channels

TL;DR

This paper explores the design of DNA storage channels, focusing on sequence reconstruction from noisy substrings, analyzing equivalence classes, and proposing asymmetric coding techniques to improve robustness against synthesis and sequencing noise.

Contribution

It introduces the concept of DNA storage channels, analyzes sequence equivalence classes, and develops new asymmetric coding methods using de Bruijn graphs and Ehrhart theory.

Findings

Number of sequence equivalence classes under noisy channels

New asymmetric coding techniques for DNA storage

Application of de Bruijn graphs and Ehrhart theory

Abstract

We consider the problem of assembling a sequence based on a collection of its substrings observed through a noisy channel. The mathematical basis of the problem is the construction and design of sequences that may be discriminated based on a collection of their substrings observed through a noisy channel. We explain the connection between the sequence reconstruction problem and the problem of DNA synthesis and sequencing, and introduce the notion of a DNA storage channel. We analyze the number of sequence equivalence classes under the channel mapping and propose new asymmetric coding techniques to combat the effects of synthesis and sequencing noise. In our analysis, we make use of restricted de Bruijn graphs and Ehrhart theory for rational polytopes.