Adversarial Torn-paper Codes

TL;DR

This paper introduces code constructions for the adversarial torn-paper channel, inspired by DNA data storage, achieving optimal rates with efficient encoding and decoding in worst-case scenarios.

Contribution

It extends previous probabilistic models to a worst-case adversarial setting and develops optimal, efficient codes for various related storage problems.

Findings

Codes achieve asymptotically optimal rate

Efficient encoding and decoding algorithms provided

Applicable to multi-strand storage and substitution errors

Abstract

We study the adversarial torn-paper channel. This problem is motivated by applications in DNA data storage where the DNA strands that carry information may break into smaller pieces which are received out of order. Our model extends the previously researched probabilistic setting to the worst-case. We develop code constructions for any parameters of the channel for which non-vanishing asymptotic rate is possible and show our constructions achieve asymptotically optimal rate while allowing for efficient encoding and decoding. Finally, we extend our results to related settings included multi-strand storage, presence of substitution errors, or incomplete coverage.