Rank modulation codes for DNA storage

TL;DR

This paper introduces a new coding scheme for DNA storage based on rank modulation, analyzing permutation feasibility and providing algorithms to generate feasible permutations to improve error tolerance.

Contribution

It presents a feasibility analysis for permutation-based coding in DNA storage and develops algorithms to generate feasible permutations for reliable data encoding.

Findings

Upper bound on feasible permutations is established.

A technique for testing permutation feasibility is devised.

An algorithm for generating feasible permutations applicable to various parameters is provided.

Abstract

Synthesis of DNA molecules offers unprecedented advances in storage technology. Yet, the microscopic world in which these molecules reside induces error patterns that are fundamentally different from their digital counterparts. Hence, to maintain reliability in reading and writing, new coding schemes must be developed. In a reading technique called shotgun sequencing, a long DNA string is read in a sliding window fashion, and a profile vector is produced. It was recently suggested by Kiah et al. that such a vector can represent the permutation which is induced by its entries, and hence a rank-modulation scheme arises. Although this interpretation suggests high error tolerance, it is unclear which permutations are feasible, and how to produce a DNA string whose profile vector induces a given permutation. In this paper, by observing some necessary conditions, an upper bound for the number of feasible permutations is given. Further, a technique for deciding the feasibility of a permutation is devised. By using insights from this technique, an algorithm for producing a considerable number of feasible permutations is given, which applies to any alphabet size and any window length.