Break-Resilient Codes with Loss Tolerance

2026-01-21

AI Summary

This work addresses the challenge posed by physical perturbations that can arbitrarily fragment codewords and erase fragments of total length up to a given limit. To this end, the paper introduces (t,s)-break resilient codes (BRCs), which enable reliable recovery of the original information even when the codeword undergoes up to t arbitrary breaks and suffers erasures of fragments whose combined length does not exceed s. The proposed framework unifies and generalizes prior models of break-resilient codes and deletion codes, establishing the first information-theoretic foundation capable of simultaneously handling both fragmentation and partial erasure. Leveraging an adversarial channel model, the authors derive a theoretical lower bound on the necessary redundancy and construct an explicit, efficient coding scheme that asymptotically approaches this bound, thereby laying the theoretical groundwork for (t,s)-BRCs.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Machine Learning: Adversarial Learning & Robustness
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Applications of cryptography
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Emerging applications in manufacturing, wireless communication, and molecular data storage require robust coding schemes that remain effective under physical distortions where codewords may be arbitrarily fragmented and partially missing. To address such challenges, we propose a new family of error-correcting codes, termed $(t,s)$-break-resilient codes ($(t,s)$-BRCs). A $(t,s)$-BRC guarantees correct decoding of the original message even after up to~$t$ arbitrary breaks of the codeword and the complete loss of some fragments whose total length is at most~$s$. This model unifies and generalizes previous approaches, extending break-resilient codes (which handle arbitrary fragmentation without fragment loss) and deletion codes (which correct bit losses in unknown positions without fragmentation) into a single information-theoretic framework. We develop a theoretical foundation for $(t,s)$-BRCs, including a formal adversarial channel model, lower bounds on the necessary redundancy, and explicit code constructions that approach these bounds.

Problem

• break-resilient codes
• deletion codes
• fragmentation
• loss tolerance
• error-correcting codes

Innovation

• break-resilient codes
• deletion codes
• fragmentation
• error-correcting codes
• information-theoretic framework