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

2025-06-22

International Symposium on Information Theory

AI Summary

This work proposes the first near-optimal error-correcting coding scheme for an adversarial torn-paper channel subject to both arbitrary fragment breaks—up to $t$ tears—and edit errors, including at most $t_e$ insertions, deletions, or substitutions. By integrating a carefully designed code construction with a joint modeling of fragment reordering and edit errors, the scheme enables efficient and reliable message recovery. Furthermore, this study establishes the first upper bound on the number of candidate codewords in list decoding under this highly fragmented setting, thereby characterizing the fundamental theoretical limits of reliable communication over such a channel.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Search and Optimization: Adversarial Search
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Security and Privacy: Applications of cryptography
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Motivated by DNA storage systems and 3D finger-printing, this work studies the adversarial noisy torn paper channel, which first applies at most $t_{e}$ edit errors (i.e., insertions, deletions, and substitutions) to the transmitted word then breaks it into $t$ + 1 fragments at arbitrary positions. Specifically, we construct a near optimal error correcting code for this channel, and refer to it by ($t, t_{e}$)-resilient code. Furthermore, we study list decoding of the noiseless torn paper channel by deriving bounds on the size of the list (of codewords) obtained from cutting a codeword of a ($t, 0$) - resilient code $t^{\prime}$ times, where $t^{\prime}> t$.

Problem

• adversarial torn paper channel
• edit errors
• error correcting code
• DNA storage
• list decoding

Innovation

• adversarial torn paper channel
• edit errors
• near-optimal error-correcting code
• list decoding
• DNA storage