A Lower Bound on the List-Decodability of Insdel Codes
Shu Liu, Ivan Tjuawinata, Chaoping Xing

TL;DR
This paper establishes a new lower bound on the list-decodability of insdel codes, revealing that previous bounds are not tight and advancing understanding of their decoding limits.
Contribution
It introduces a novel lower bound for insdel code list-decodability, improving upon previous bounds and addressing an open problem in the field.
Findings
The new bound is not tight, unlike the Johnson bound for other metrics.
If a code's list decoding radius is below this bound, it must be list-decodable with a given list size.
Application of the bound to well-known codes provides new insights into their insdel-list-decodability.
Abstract
For codes equipped with metrics such as Hamming metric, symbol pair metric or cover metric, the Johnson bound guarantees list-decodability of such codes. That is, the Johnson bound provides a lower bound on the list-decoding radius of a code in terms of its relative minimum distance , list size and the alphabet size For study of list-decodability of codes with insertion and deletion errors (we call such codes insdel codes), it is natural to ask the open problem whether there is also a Johnson-type bound. The problem was first investigated by Wachter-Zeh and the result was amended by Hayashi and Yasunaga where a lower bound on the list-decodability for insdel codes was derived. The main purpose of this paper is to move a step further towards solving the above open problem. In this work, we provide a new lower bound for the list-decodability of an insdel code. As a…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsDNA and Biological Computing · Advanced biosensing and bioanalysis techniques · Coding theory and cryptography
