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arXiv · 1506.00740

Asymmetric Lee Distance Codes for DNA-Based Storage

Ryan Gabrys·Han Mao Kiah·Olgica Milenkovic
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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.

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Ryan Gabrys, Han Mao Kiah, Olgica Milenkovic. 2015-06-02. Asymmetric Lee Distance Codes for DNA-Based Storage. https://arxiv.org/abs/1506.00740

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