On Lattice Packings and Coverings of Asymmetric Limited-Magnitude Balls

Hengjia Wei, Xin Wang, Moshe Schwartz

Research output: Contribution to journalArticlepeer-review

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 languageAmerican English
Article number9393979
Pages (from-to)5104-5115
Number of pages12
JournalIEEE Transactions on Information Theory
Volume67
Issue number8
DOIs
StatePublished - 1 Aug 2021

Keywords

  • Integer coding
  • covering
  • lattices
  • limited-magnitude errors
  • packing
  • tiling

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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