Duplication-Correcting Codes for Data Storage in the DNA of Living Organisms

TL;DR

This paper introduces error-correcting codes specifically designed to address tandem duplication mutations in DNA data storage, improving data integrity in biological media.

Contribution

It presents two families of codes for correcting tandem duplication errors, including fixed-length and bounded errors, and classifies duplication lengths for unique decoding.

Findings

Codes can correct tandem duplication errors of fixed length.

Codes for correcting bounded number of errors are developed.

Complete classification of duplication lengths for unique roots.

Abstract

The ability to store data in the DNA of a living organism has applications in a variety of areas including synthetic biology and watermarking of patented genetically-modified organisms. Data stored in this medium is subject to errors arising from various mutations, such as point mutations, indels, and tandem duplication, which need to be corrected to maintain data integrity. In this paper, we provide error-correcting codes for errors caused by tandem duplications, which create a copy of a block of the sequence and insert it in a tandem manner, i.e., next to the original. In particular, we present two families of codes for correcting errors due to tandem-duplications of a fixed length, the first family can correct any number of errors while the second corrects a bounded number of errors. We also study codes for correcting tandem duplications of length up to a given constant $k$, where we are primarily focused on the cases of $k=2,3$. Finally, we provide a full classification of the sets of lengths allowed in tandem duplication that result in a unique root for all sequences.