On Lattice Packings and Coverings of Asymmetric Limited-Magnitude Balls

Hengjia Wei; Xin Wang; Moshe Schwartz

doi:10.1109/TIT.2021.3070462

On Lattice Packings and Coverings of Asymmetric Limited-Magnitude Balls

Hengjia Wei, Xin Wang, Moshe Schwartz

Department of Electrical & Computer Engineering

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We construct integer error-correcting codes and covering codes for the limited-magnitude error channel with more than one error. The codes are lattices that pack or cover the space with the appropriate error ball. Some of the constructions attain an asymptotic packing/covering density that is constant. The results are obtained via various methods, including the use of codes in the Hamming metric, modular ${B}_{{t}}$-sequences, 2-fold Sidon sets, and sets avoiding arithmetic progression.

Original language	English
Article number	9393979
Pages (from-to)	5104-5115
Number of pages	12
Journal	IEEE Transactions on Information Theory
Volume	67
Issue number	8
DOIs	https://doi.org/10.1109/TIT.2021.3070462
State	Published - 1 Aug 2021

Keywords

Integer coding
covering
lattices
limited-magnitude errors
packing
tiling

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2021.3070462

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abstract = "We construct integer error-correcting codes and covering codes for the limited-magnitude error channel with more than one error. The codes are lattices that pack or cover the space with the appropriate error ball. Some of the constructions attain an asymptotic packing/covering density that is constant. The results are obtained via various methods, including the use of codes in the Hamming metric, modular ${B}_{{t}}$-sequences, 2-fold Sidon sets, and sets avoiding arithmetic progression.",

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AU - Schwartz, Moshe

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N2 - We construct integer error-correcting codes and covering codes for the limited-magnitude error channel with more than one error. The codes are lattices that pack or cover the space with the appropriate error ball. Some of the constructions attain an asymptotic packing/covering density that is constant. The results are obtained via various methods, including the use of codes in the Hamming metric, modular ${B}_{{t}}$-sequences, 2-fold Sidon sets, and sets avoiding arithmetic progression.

AB - We construct integer error-correcting codes and covering codes for the limited-magnitude error channel with more than one error. The codes are lattices that pack or cover the space with the appropriate error ball. Some of the constructions attain an asymptotic packing/covering density that is constant. The results are obtained via various methods, including the use of codes in the Hamming metric, modular ${B}_{{t}}$-sequences, 2-fold Sidon sets, and sets avoiding arithmetic progression.

KW - Integer coding

KW - covering

KW - lattices

KW - limited-magnitude errors

KW - packing

KW - tiling

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On Lattice Packings and Coverings of Asymmetric Limited-Magnitude Balls

Abstract

Keywords

ASJC Scopus subject areas

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