Non-binary GLD codes and their lattices

Nicola Di Pietro, Nour Basha, Joseph Boutros

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

Abstract

The recently discovered family of generalized low-density (GLD) lattices brings new mathematical challenges to coding theorists and practitioners. Given the excellent performance of integer GLD lattices in high dimensions and motivated by the simple lattice structure used for fast iterative decoding, this paper is a first attempt to analyze GLD lattices for asymptotically large dimensions. Firstly, we describe non-binary GLD codes and show their asymptotic goodness in terms of minimum Hamming distance. Secondly, we consider a GLD lattice ensemble built via Construction A from non-binary GLD codes, and analyze their goodness with respect to Poltyrev limit on the Gaussian channel. Finally, at large dimensions and using a large code alphabet, we prove that infinite GLD lattice constellations attain Poltyrev capacity limit under maximum likelihood decoding.

Original languageEnglish
Title of host publication2015 IEEE Information Theory Workshop, ITW 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781479955268
DOIs
Publication statusPublished - 1 Jan 2015
Event2015 IEEE Information Theory Workshop, ITW 2015 - Jerusalem, Israel
Duration: 26 Apr 20151 May 2015

Other

Other2015 IEEE Information Theory Workshop, ITW 2015
CountryIsrael
CityJerusalem
Period26/4/151/5/15

Fingerprint

Hamming distance
Iterative decoding
Maximum likelihood
Decoding

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Networks and Communications
  • Information Systems
  • Computational Theory and Mathematics

Cite this

Di Pietro, N., Basha, N., & Boutros, J. (2015). Non-binary GLD codes and their lattices. In 2015 IEEE Information Theory Workshop, ITW 2015 [7133127] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ITW.2015.7133127

Non-binary GLD codes and their lattices. / Di Pietro, Nicola; Basha, Nour; Boutros, Joseph.

2015 IEEE Information Theory Workshop, ITW 2015. Institute of Electrical and Electronics Engineers Inc., 2015. 7133127.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Di Pietro, N, Basha, N & Boutros, J 2015, Non-binary GLD codes and their lattices. in 2015 IEEE Information Theory Workshop, ITW 2015., 7133127, Institute of Electrical and Electronics Engineers Inc., 2015 IEEE Information Theory Workshop, ITW 2015, Jerusalem, Israel, 26/4/15. https://doi.org/10.1109/ITW.2015.7133127
Di Pietro N, Basha N, Boutros J. Non-binary GLD codes and their lattices. In 2015 IEEE Information Theory Workshop, ITW 2015. Institute of Electrical and Electronics Engineers Inc. 2015. 7133127 https://doi.org/10.1109/ITW.2015.7133127
Di Pietro, Nicola ; Basha, Nour ; Boutros, Joseph. / Non-binary GLD codes and their lattices. 2015 IEEE Information Theory Workshop, ITW 2015. Institute of Electrical and Electronics Engineers Inc., 2015.
@inproceedings{7bee9cc20c654d57a564c86bedce7eb8,
title = "Non-binary GLD codes and their lattices",
abstract = "The recently discovered family of generalized low-density (GLD) lattices brings new mathematical challenges to coding theorists and practitioners. Given the excellent performance of integer GLD lattices in high dimensions and motivated by the simple lattice structure used for fast iterative decoding, this paper is a first attempt to analyze GLD lattices for asymptotically large dimensions. Firstly, we describe non-binary GLD codes and show their asymptotic goodness in terms of minimum Hamming distance. Secondly, we consider a GLD lattice ensemble built via Construction A from non-binary GLD codes, and analyze their goodness with respect to Poltyrev limit on the Gaussian channel. Finally, at large dimensions and using a large code alphabet, we prove that infinite GLD lattice constellations attain Poltyrev capacity limit under maximum likelihood decoding.",
author = "{Di Pietro}, Nicola and Nour Basha and Joseph Boutros",
year = "2015",
month = "1",
day = "1",
doi = "10.1109/ITW.2015.7133127",
language = "English",
booktitle = "2015 IEEE Information Theory Workshop, ITW 2015",
publisher = "Institute of Electrical and Electronics Engineers Inc.",

}

TY - GEN

T1 - Non-binary GLD codes and their lattices

AU - Di Pietro, Nicola

AU - Basha, Nour

AU - Boutros, Joseph

PY - 2015/1/1

Y1 - 2015/1/1

N2 - The recently discovered family of generalized low-density (GLD) lattices brings new mathematical challenges to coding theorists and practitioners. Given the excellent performance of integer GLD lattices in high dimensions and motivated by the simple lattice structure used for fast iterative decoding, this paper is a first attempt to analyze GLD lattices for asymptotically large dimensions. Firstly, we describe non-binary GLD codes and show their asymptotic goodness in terms of minimum Hamming distance. Secondly, we consider a GLD lattice ensemble built via Construction A from non-binary GLD codes, and analyze their goodness with respect to Poltyrev limit on the Gaussian channel. Finally, at large dimensions and using a large code alphabet, we prove that infinite GLD lattice constellations attain Poltyrev capacity limit under maximum likelihood decoding.

AB - The recently discovered family of generalized low-density (GLD) lattices brings new mathematical challenges to coding theorists and practitioners. Given the excellent performance of integer GLD lattices in high dimensions and motivated by the simple lattice structure used for fast iterative decoding, this paper is a first attempt to analyze GLD lattices for asymptotically large dimensions. Firstly, we describe non-binary GLD codes and show their asymptotic goodness in terms of minimum Hamming distance. Secondly, we consider a GLD lattice ensemble built via Construction A from non-binary GLD codes, and analyze their goodness with respect to Poltyrev limit on the Gaussian channel. Finally, at large dimensions and using a large code alphabet, we prove that infinite GLD lattice constellations attain Poltyrev capacity limit under maximum likelihood decoding.

UR - http://www.scopus.com/inward/record.url?scp=84938945532&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84938945532&partnerID=8YFLogxK

U2 - 10.1109/ITW.2015.7133127

DO - 10.1109/ITW.2015.7133127

M3 - Conference contribution

BT - 2015 IEEE Information Theory Workshop, ITW 2015

PB - Institute of Electrical and Electronics Engineers Inc.

ER -