Multiple Criss-Cross Deletion-Correcting Codes

Lorenz Welter, Rawad Bitar, Antonia Wachter-Zeh, Eitan Yaakobi

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

Abstract

This paper investigates the problem of correcting multiple criss-cross deletions in arrays. More precisely, we study the unique recovery of n\times n arrays affected by any combination of t_{\mathrm{r}} row and t_{\mathrm{c}} column deletions such that t_{\mathrm{r}}+t_{\mathrm{c}}=t for a given t. We refer to these type of deletions as t-criss-cross deletions. We show that the asymptotic redundancy of a code correcting t-criss-cross deletions is at least tn+t\log n-\log(t!). Then, we present an existential construction of a code capable of correcting t-criss-cross deletions where its redundancy is bounded from above by tn+\mathcal{O}(t^{2}\log^{2}n). The main ingredients of the presented code are systematic binary t-deletion-correcting codes and Gabidulin codes. The first ingredient helps locating the indices of the deleted rows and columns, thus transforming the deletion-correction problem into an erasure-correction problem which is then solved using the second ingredient.

Original languageEnglish
Title of host publication2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
Pages2798-2803
Number of pages6
ISBN (Electronic)9781538682098
DOIs
StatePublished - 12 Jul 2021
Event2021 IEEE International Symposium on Information Theory, ISIT 2021 - Virtual, Melbourne, Australia
Duration: 12 Jul 202120 Jul 2021

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2021-July

Conference

Conference2021 IEEE International Symposium on Information Theory, ISIT 2021
Country/TerritoryAustralia
CityVirtual, Melbourne
Period12/07/2120/07/21

All Science Journal Classification (ASJC) codes

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

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