Correcting Tail Deletions in Rank Modulated Composite Encoding for Data Storage in DNA

TL;DR

This paper explores combining composite DNA encoding with rank modulation to improve data storage, focusing on deletion and insertion error correction in DNA-based data encoding.

Contribution

It introduces new bounds and constructions for codes over partial permutations to correct deletions and insertions in DNA data storage systems.

Findings

Developed bounds for deletion and insertion codes in DNA storage.

Constructed efficient codes over partial permutations for error correction.

Enhanced understanding of rank modulation codes in DNA data encoding.

Abstract

We study the combination of two recent coding approaches, in the context of DNA based data storage. Composite DNA alphabets leverage properties of the DNA synthesis and sequencing process. A composite symbol does not represent a single nucleotide, but rather a designed mixture of DNA nucleotides. Using the high multiplicity that is intrinsic to synthesis and sequencing a composite symbol consists of frequencies in the mixture. Rank modulation codes use permutations to represent information. Combining the two, we construct encoding that uses permutations of nucleotide frequencies rather than the exact frequency values. Codes for this approach were addressed in previous work, under Kendall's tau distances. In this work we study deletion and insertion codes. We present bounds and constructions of efficient codes defined over partial permutations.