Non-Binary GLD Codes and their Lattices Conference Paper

abstract

• 2015 IEEE. 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.

name of conference

• 2015 IEEE Information Theory Workshop (ITW)

authors

• Boutros, Joseph

published proceedings

• 2015 IEEE INFORMATION THEORY WORKSHOP (ITW)

author list (cited authors)

• di Pietro, N., Basha, N., & Boutros, J. J.

citation count

• 7

complete list of authors

• di Pietro, Nicola||Basha, Nour||Boutros, Joseph J

publication date

• April 2015

publisher

• Institute of Electrical and Electronics Engineers (IEEE)  Publisher

Digital Object Identifier (DOI)

• 10.1109/itw.2015.7133127

International Standard Book Number (ISBN) 13

• 9781479955268

start page

• 1

end page

• 5

URL

• https://ieeexplore.ieee.org/xpl/conhome/7123792/proceeding