Codes correcting a burst of deletions or insertions

Clayton Schoeny, Antonia Wachter-Zeh, Ryan Gabrys, Eitan Yaakobi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

This paper studies codes that correct bursts of deletions. Namely, a code will be called a b-burst-correcting code if it can correct a deletion of any b consecutive bits. While the lower bound on the redundancy of such codes was shown by Levenshtein to be asymptotically log(n) + b - 1, the redundancy of the best code construction by Cheng et al. is b(log(n/b + 1)). In this paper we close on this gap and provide codes with redundancy at most log(n) + (b - 1) log(log(n)) + b - log(b). We also extend the burst deletion model to two more cases: 1. a deletion burst of at most b consecutive bits and 2. a deletion burst of size at most b (not necessarily consecutive). We extend our code construction for the first case and study the second case for b = 3, 4. The equivalent models for insertions are also studied and are shown to be equivalent to correcting the corresponding burst of deletions.

Original languageEnglish
Title of host publicationProceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
Pages630-634
Number of pages5
ISBN (Electronic)9781509018062
DOIs
StatePublished - 10 Aug 2016
Event2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain
Duration: 10 Jul 201615 Jul 2016

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2016-August

Conference

Conference2016 IEEE International Symposium on Information Theory, ISIT 2016
Country/TerritorySpain
CityBarcelona
Period10/07/1615/07/16

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modelling and Simulation
  • Applied Mathematics

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