Upper Bounds on Multiple $b$-Burst Deletion-Correcting Codes

2026-05-31

AI Summary

This work addresses the fundamental limits of error-correcting codes capable of correcting multiple $b$-burst deletions, a critical requirement in applications such as DNA data storage. By conducting a detailed structural analysis of multi-burst deletion balls and leveraging tools from combinatorics and information theory, the authors derive several tighter upper bounds and an effective combinatorial lower bound on the maximum possible code size. These bounds improve upon existing results across general parameter regimes and achieve asymptotic optimality in certain specific cases, thereby providing a more precise characterization of the theoretical performance limits for codes correcting multiple burst deletions.

Abstract

Motivated by their applications in DNA-based storage systems, codes capable of correcting consecutive deletions have attracted significant attention. An important class of such codes consists of those that can correct multiple consecutive deletion errors, commonly referred to as multiple $b$-burst deletion-correcting codes. In this paper, we investigate the fundamental limits of multiple $b$-burst deletion-correcting codes. Specifically, we first characterize several structural properties of the associated deletion balls. Then, leveraging these properties, we derive several upper bounds and a combinatorial lower bound on the maximum size of such codes. As a consequence, our bounds improve upon the previously known results for general parameter regimes and are shown to be asymptotically optimal for certain cases.

Problem

• burst deletion
• deletion-correcting codes
• upper bounds
• DNA storage
• combinatorial bounds

Innovation

• burst deletion-correcting codes
• deletion balls
• upper bounds
• combinatorial bounds
• DNA-based storage