Near Optimal Code Construction for the Adversarial Torn Paper Channel With Edit Errors

TL;DR

This paper introduces a near-optimal error-correcting code for the adversarial torn paper channel with edit errors, relevant to DNA storage and 3D fingerprinting, capable of reconstructing original data from fragmented, error-prone pieces.

Contribution

It presents a novel code construction that is resilient to both edit errors and arbitrary fragment breaks, advancing error correction for complex, adversarial channels.

Findings

Constructed near-optimal codes for torn paper channels with edit errors.

Derived bounds on list decoding size for multiple fragmentations.

Demonstrated applicability to DNA storage and fingerprinting systems.

Abstract

Motivated by DNA storage systems and 3D fingerprinting, this work studies the adversarial torn paper channel with edit errors. This channel first applies at most $t_e$ edit errors (i.e., insertions, deletions, and substitutions) to the transmitted word and then breaks it into $t+1$ fragments at arbitrary positions. In this paper, we construct a near optimal error correcting code for this channel, which will be referred to as a $t$-breaks $t_e$-edit-errors resilient code. This code enables reconstructing the transmitted codeword from the $t+1$ noisy fragments. Moreover, we study list decoding of the torn paper channel by deriving bounds on the size of the list (of codewords) obtained from cutting a codeword of a $t$-breaks resilient code $t'$ times, where $t' > t$.