On tilings of asymmetric limited-magnitude balls

Hengjia Wei; Moshe Schwartz

doi:10.1109/ITW46852.2021.9457590

On tilings of asymmetric limited-magnitude balls

Hengjia Wei, Moshe Schwartz

Department of Electrical & Computer Engineering

Ben-Gurion University of the Negev

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-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 language	American English
Title of host publication	IEEE Information Theory Workshop, ITW 2020
Pages	1-5
Number of pages	5
ISBN (Electronic)	9781728159621
DOIs	https://doi.org/10.1109/ITW46852.2021.9457590
State	Published - 22 Jun 2021
Event	2020 IEEE Information Theory Workshop, ITW 2020 - Virtual, Riva del Garda, Italy Duration: 11 Apr 2021 → 15 Apr 2021

Conference

Conference	2020 IEEE Information Theory Workshop, ITW 2020
Country/Territory	Italy
City	Virtual, Riva del Garda
Period	11/04/21 → 15/04/21

All Science Journal Classification (ASJC) codes

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

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10.1109/ITW46852.2021.9457590

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title = "On tilings of asymmetric limited-magnitude balls",

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.",

author = "Hengjia Wei and Moshe Schwartz",

note = "Funding Information: This work was supported in part by an Israel Science Foundation (ISF) grant 270/18. Publisher Copyright: {\textcopyright}2021 IEEE; 2020 IEEE Information Theory Workshop, ITW 2020 ; Conference date: 11-04-2021 Through 15-04-2021",

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N2 - 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.

AB - 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.

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DO - 10.1109/ITW46852.2021.9457590

M3 - Conference contribution

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T2 - 2020 IEEE Information Theory Workshop, ITW 2020

Y2 - 11 April 2021 through 15 April 2021

ER -

On tilings of asymmetric limited-magnitude balls

Abstract

Conference

All Science Journal Classification (ASJC) codes

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