Error-correcting Codes for Noisy Duplication Channels

TL;DR

This paper develops error-correcting codes for DNA data storage that can handle both exact and noisy tandem duplication errors, ensuring data integrity despite complex error patterns.

Contribution

It introduces novel codes capable of correcting multiple exact duplications and a single noisy duplication, based on duplication root recovery, with proven asymptotic optimality.

Findings

Codes correct multiple exact duplications.

Codes correct one noisy duplication with substitution noise.

Construction is asymptotically optimal.

Abstract

Because of its high data density and longevity, DNA is emerging as a promising candidate for satisfying increasing data storage needs. Compared to conventional storage media, however, data stored in DNA is subject to a wider range of errors resulting from various processes involved in the data storage pipeline. In this paper, we consider correcting duplication errors for both exact and noisy tandem duplications of a given length k. An exact duplication inserts a copy of a substring of length k of the sequence immediately after that substring, e.g., ACGT to ACGACGT, where k = 3, while a noisy duplication inserts a copy suffering from substitution noise, e.g., ACGT to ACGATGT. Specifically, we design codes that can correct any number of exact duplication and one noisy duplication errors, where in the noisy duplication case the copy is at Hamming distance 1 from the original. Our constructions rely upon recovering the duplication root of the stored codeword. We characterize the ways in which duplication errors manifest in the root of affected sequences and design efficient codes for correcting these error patterns. We show that the proposed construction is asymptotically optimal, in the sense that it has the same asymptotic rate as optimal codes correcting exact duplications only.