Sequence-Subset Distance and Coding for Error Control in DNA-based Data Storage

Abstract

The process of DNA-based data storage (DNA storage for short) can be mathematically modelled as a communication channel, termed DNA storage channel, whose inputs and outputs are sets of unordered sequences. To design error correcting codes for DNA storage channel, a new metric, termed the sequence-subset distance, is introduced, which generalizes the Hamming distance to a distance function defined between any two sets of unordered vectors and helps to establish a uniform framework to design error correcting codes for DNA storage channel. We further introduce a family of error correcting codes, referred to as \emph{sequence-subset codes}, for DNA storage and show that the error-correcting ability of such codes is completely determined by their minimum distance. We derive some upper bounds on the size of the sequence-subset codes including a tight bound for a special case, a Singleton-like bound and a Plotkin-like bound. We also propose some constructions, including an optimal construction for that special case, which imply lower bounds on the size of such codes.

This paper has been accepted for publication by IEEE Transactions on Information Theory