Break-Resilient Codes with Loss Tolerance

TL;DR

This paper introduces a new class of error-correcting codes called $(t,s)$-break-resilient codes that can handle multiple arbitrary breaks and fragment losses in data transmission, unifying previous models.

Contribution

It formalizes the $(t,s)$-break-resilient codes, providing theoretical bounds and explicit constructions that approach optimal redundancy, extending existing break-resilient and deletion codes.

Findings

Established lower bounds on redundancy for $(t,s)$-BRCs

Developed explicit code constructions approaching these bounds

Unified previous break-resilient and deletion coding models

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.