On tilings of asymmetric limited-magnitude balls

Hengjia Wei, Moshe Schwartz

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

Abstract

We study whether an asymmetric limited-magnitude ball may tile Zn. This ball generalizes previously studied shapes: crosses, semi-crosses, and quasi-crosses. Such tilings act as perfect error-correcting codes in a channel which changes a transmitted integer vector in a bounded number of entries by limited-magnitude errors. A construction of lattice tilings based on perfect codes in the Hamming metric is given. Several non-existence results are proved, both for general tilings, and lattice tilings. A complete classification of lattice tilings for two certain cases is proved.

Original languageEnglish
Title of host publication2020 IEEE Information Theory Workshop, ITW 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781728159621
DOIs
StatePublished - 11 Apr 2021
Event2020 IEEE Information Theory Workshop, ITW 2020 - Virtual, Riva del Garda, Italy
Duration: 11 Apr 202115 Apr 2021

Publication series

Name2020 IEEE Information Theory Workshop, ITW 2020

Conference

Conference2020 IEEE Information Theory Workshop, ITW 2020
Country/TerritoryItaly
CityVirtual, Riva del Garda
Period11/04/2115/04/21

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Information Systems
  • Signal Processing
  • Software
  • Theoretical Computer Science

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