Upper Bounds on Multiple $b$-Burst Deletion-Correcting Codes
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918534329663488 |
|---|---|
| author | Wang, Chen Kong, Xiangliang Yaakobi, Eitan Duman, Tolga M. |
| author_facet | Wang, Chen Kong, Xiangliang Yaakobi, Eitan Duman, Tolga M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01245 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Upper Bounds on Multiple $b$-Burst Deletion-Correcting Codes Wang, Chen Kong, Xiangliang Yaakobi, Eitan Duman, Tolga M. Information Theory Combinatorics 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. |
| title | Upper Bounds on Multiple $b$-Burst Deletion-Correcting Codes |
| topic | Information Theory Combinatorics |
| url | https://arxiv.org/abs/2606.01245 |