Error-Correcting Codes for Two Bursts of t1-Deletion-t2-Insertion with Reduced Complexity
Year: 2026
Type: preprint
Abstract: Burst errors involving simultaneous insertions, deletions, and substitutions occur in practical scenarios, including DNA data storage and document synchronization, motivating the development of channel codes that can correct such errors. In this paper, we construct error-correcting codes (ECCs) capable of handling multiple bursts of t1-deletion-t2-insertion ((t1, t2)-DI) errors, where each burst consists of t1 deletions followed by t2 insertions in a binary sequence. We make three key contributions: First, we establish the fundamental equivalence among (i) ECCs correcting two bursts of (t1, t2)-DI errors, (ii) ECCs correcting two bursts of (t2, t1)-DI errors, and (iii) ECCs correcting one burst of (t1, t2)-DI together with one burst of (t2, t1)-DI errors. Then, we derive lower and upper bounds on the code size of two-burst (t1, t2)-DI ECCs, which can naturally be extended to the case of multiple bursts. Finally, we present constructions of ECCs correcting two bursts of (t1, t2)-DI errors. Compared with codes obtained via the direct application of the syndrome compression technique, the proposed constructions achieve substantially improved computational efficiency.
Source: arXiv (Cornell University)
Authors: Liu, Yajuan, Duman, Tolga M.
Institution: Bilkent University
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7124430189
Cites:
Cited by:
Related to: