Asymmetric Lee Distance Codes for DNA-Based Storage
Information Theory
2016-12-16 v5 math.IT
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.
Cite
@article{arxiv.1506.00740,
title = {Asymmetric Lee Distance Codes for DNA-Based Storage},
author = {Ryan Gabrys and Han Mao Kiah and Olgica Milenkovic},
journal= {arXiv preprint arXiv:1506.00740},
year = {2016}
}