A New Version of q-ary Varshamov-Tenengolts Codes with More Efficient Encoders: The Differential VT Codes and The Differential Shifted VT Codes

TL;DR

This paper introduces new q-ary codes, specifically differential VT and shifted VT codes, that efficiently correct burst insertions and deletions in DNA storage, offering improved encoding efficiency over existing methods.

Contribution

The work presents novel differential VT and shifted VT codes that directly operate on q-ary sequences, reducing redundancy and improving encoding efficiency for DNA data storage applications.

Findings

Codes effectively correct burst insertions/deletions in DNA storage.

Proposed encoders have lower redundancy than previous methods.

Direct q-ary decoding improves efficiency over binary-based approaches.

Abstract

The problem of correcting deletions and insertions has recently received significantly increased attention due to the DNA-based data storage technology, which suffers from deletions and insertions with extremely high probability. In this work, we study the problem of constructing non-binary burst-deletion/insertion correcting codes. Particularly, for the quaternary alphabet, our designed codes are suited for correcting a burst of deletions/insertions in DNA storage. Non-binary codes correcting a single deletion or insertion were introduced by Tenengolts [1984], and the results were extended to correct a fixed-length burst of deletions or insertions by Schoeny et al. [2017]. Recently, Wang et al. [2021] proposed constructions of non-binary codes of length n, correcting a burst of length at most two for q-ary alphabets with redundancy log n+O(log q log log n) bits, for arbitrary even q. The common idea in those constructions is to convert non-binary sequences into binary sequences, and the error decoding algorithms for the q-ary sequences are mainly based on the success of recovering the corresponding binary sequences, respectively. In this work, we look at a natural solution in which the error detection and correction algorithms are performed directly over q-ary sequences, and for certain cases, our codes provide a more efficient encoder with lower redundancy than the best-known encoder in the literature.