New Bounds for GLD Lattices and Codes

Maiara F. Bollauf, Joseph J. Boutros, Nordine Mir

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

Abstract

We prove that the ensemble of random Generalized Low-Density (GLD) lattices can attain the Poltyrev limit for an alphabet size increasing polylogarithmically with the lattice dimension. Our main theorem imposes no constraints on the normalized minimum distance of the code associated to the lattice ensemble, any asymptotically good code is suitable. This is a great improvement with respect to the first theorem on Poltyrev goodness of GLD lattices (2015). Our new bound is based on a new method referred to as the buckets approach where we employ the asymptotics of the restricted compositions of the Hamming weight. The new bound has applications in many coding areas beyond the specific lattice ensemble considered in this paper.

Original languageEnglish
Title of host publication2019 IEEE Information Theory Workshop, ITW 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781538669006
DOIs
Publication statusPublished - Aug 2019
Event2019 IEEE Information Theory Workshop, ITW 2019 - Visby, Sweden
Duration: 25 Aug 201928 Aug 2019

Publication series

Name2019 IEEE Information Theory Workshop, ITW 2019

Conference

Conference2019 IEEE Information Theory Workshop, ITW 2019
CountrySweden
CityVisby
Period25/8/1928/8/19

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ASJC Scopus subject areas

  • Software
  • Computational Theory and Mathematics
  • Computer Networks and Communications
  • Information Systems

Cite this

Bollauf, M. F., Boutros, J. J., & Mir, N. (2019). New Bounds for GLD Lattices and Codes. In 2019 IEEE Information Theory Workshop, ITW 2019 [8989412] (2019 IEEE Information Theory Workshop, ITW 2019). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ITW44776.2019.8989412