Asymmetric Lee Distance Codes for DNA-Based Storage

TL;DR

This paper introduces asymmetric Lee distance codes for DNA storage, combining Lee and Hamming distances, providing bounds and constructions to improve error correction in DNA-based data systems.

Contribution

It defines a new distance metric, derives bounds, and proposes code constructions for DNA storage systems, advancing error correction methods.

Findings

Derived upper bounds on code size using linear programming

Proposed code constructions for lower bounds

Demonstrated the metric's relation to Lee and Hamming distances

Abstract

We consider a new family of codes, termed asymmetric Lee distance codes, that arise in the design and implementation of DNA-based storage systems and systems with parallel string transmission protocols. The codewords are defined over a quaternary alphabet, although the results carry over to other alphabet sizes; furthermore, symbol confusability is dictated by their underlying binary representation. Our contributions are two-fold. First, we demonstrate that the new distance represents a linear combination of the Lee and Hamming distance and derive upper bounds on the size of the codes under this metric based on linear programming techniques. Second, we propose a number of code constructions which imply lower bounds.