Abstract
Advances in synthesis and sequencing technologies have made DNA macromolecules an attractive medium for digital information storage. Compared with the ex vivo method that stores data in a non-biological environment, there have been considerations and attempts to store data in living organisms, also known as the in vivo method or live DNA due to several magnificent advantages. Data stored in this medium is prone to errors arising from various mutations such as point mutations (when there is a change in a single nucleotide in DNA, i.e. deletion, insertion, or substitution) or chromosomal alterations (that change the structure of a segment of DNA, i.e. tandem duplication, inversion).In this paper, we provide error-correcting codes for errors caused by inversions, that reverse the order of a segment of DNA. In particular, we construct families of codes for correcting single inversion of a fixed length or variable length up to a given constant k with at most log n+Θ(1) redundant bits, where the redundancy matches the optimal value up to only a constant additive term. Moreover, our codes remain order-optimal, i.e. the redundancy is at most log n + o(log n), when k = o(log n). The redundancy can be further reduced when k ≪ 3.