New results on low-density integer lattices

Nicola Di Pietro, Joseph Boutros, Gilles Zémor, Loïc Brunei

Research output: Contribution to conferencePaper

6 Citations (Scopus)

Abstract

A new family of integer lattices built from Construction A and non-binary low-density parity-check (LDPC) codes has been proposed by the authors in 2012. Lattices in this family are referred to as LDA lattices. Previous experimental results revealed excellent performance which clearly single out LDA lattices among the strongest candidates for potential applications in digital communications and networks, such as network coding and information theoretic security at the physical layer level. In this paper, we show that replacing random codes by LDPC codes in Construction A does not induce any structural loss. More precisely, our main theorem states that LDA lattices can achieve Poltyrev capacity limit on an additive white Gaussian noise channel. We present here the detailed proof and its consequences on the lattice dimension, the finite field size, and the parameters of the LDPC ensemble. The latter has a row weight that increases logarithmically in the code length. In a more recent work, it is proved that the Poltyrev limit is attained by a different LDA ensemble having a small constant row weight.

Original languageEnglish
Pages39-44
Number of pages6
DOIs
Publication statusPublished - 16 May 2013
Event2013 Information Theory and Applications Workshop, ITA 2013 - San Diego, CA, United States
Duration: 10 Feb 201315 Feb 2013

Other

Other2013 Information Theory and Applications Workshop, ITA 2013
CountryUnited States
CitySan Diego, CA
Period10/2/1315/2/13

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ASJC Scopus subject areas

  • Computer Science Applications
  • Information Systems

Cite this

Di Pietro, N., Boutros, J., Zémor, G., & Brunei, L. (2013). New results on low-density integer lattices. 39-44. Paper presented at 2013 Information Theory and Applications Workshop, ITA 2013, San Diego, CA, United States. https://doi.org/10.1109/ITA.2013.6502926