Leech Constellations of Construction-A Lattices

Nicola Di Pietro, Joseph Boutros

Research output: Contribution to journalArticle

7 Citations (Scopus)


The problem of communicating over the additive white Gaussian noise (AWGN) channel with lattice codes is addressed in this paper. Theoretically, Voronoi constellations have proved to yield very powerful lattice codes when the fine/coding lattice is AWGN-good and the coarse/shaping lattice has an optimal shaping gain. However, achieving Shannon capacity with these premises and practically implementable encoding algorithms is in general not an easy task. In this paper, a new way to encode and demap Construction-A Voronoi lattice codes is presented. As a meaningful application of this scheme, the second part of the paper is focused on Leech constellations of low-density Construction-A (LDA) lattices: LDA Voronoi lattice codes are presented whose numerically measured waterfall region is situated at less than 0.8 dB from Shannon capacity. These LDA lattice codes are based on dual-diagonal nonbinary low-density parity-check codes. With this choice, encoding, iterative decoding, and demapping have all linear complexity in the block length.

Original languageEnglish
Article number8003329
Pages (from-to)4622-4631
Number of pages10
JournalIEEE Transactions on Communications
Issue number11
Publication statusPublished - 1 Nov 2017
Externally publishedYes


  • Construction A
  • Dual-diagonal LDPC codes
  • LDA lattices
  • Leech lattice
  • Voronoi constellations

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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