Break-Resilient Codes

TL;DR

This paper studies break-resilient codes capable of reconstructing data despite adversarial damage at up to t positions, establishing bounds and constructing optimal codes with relevance to DNA data storage.

Contribution

It provides lower bounds on redundancy and constructs codes that are asymptotically optimal for the break-resilient coding problem.

Findings

Established lower bounds on redundancy for break-resilient codes.

Designed code constructions that asymptotically meet these bounds.

Linked the problem to the torn paper channel in DNA data storage.

Abstract

We investigate the problem of encoding data into an $(n, t)$-break-resilient code ($(n, t)$-BRC), i.e., a collections of sequences of length~$n$ from which the original data can be reconstructed even if they are adversarially broken at up to~$t$ arbitrary positions. We establish lower bounds on the redundancy of any $(n, t)$-BRC and present code constructions that meet these bounds up to asymptotically negligible terms. Interestingly, this problem shares similarities with the recently studied torn paper channel, which has emerged in the context of DNA data storage.