Improved Rank-Modulation Codes for DNA Storage with Shotgun Sequencing

TL;DR

This paper introduces improved rank-modulation codes for DNA storage that utilize shotgun sequencing, providing systematic and non-systematic codes with optimal size and efficient encoding, ensuring reliable data retrieval from DNA sequences.

Contribution

The paper presents novel systematic and non-systematic rank-modulation codes for DNA storage with shotgun sequencing, achieving optimal size and efficient encoding algorithms.

Findings

Constructed systematic codes with efficient encoding.

Proved the codes are optimal in size.

DNA sequence length is polynomial in code parameters.

Abstract

We study permutations over the set of $\ell$-grams, that are feasible in the sense that there is a sequence whose $\ell$-gram frequency has the same ranking as the permutation. Codes, which are sets of feasible permutations, protect information stored in DNA molecules using the rank-modulation scheme, and read using the shotgun sequencing technique. We construct systematic codes with an efficient encoding algorithm, and show that they are optimal in size. The length of the DNA sequences that correspond to the codewords is shown to be polynomial in the code parameters. Non-systematic with larger size are also constructed.