Annales Des Télécommunications

, Volume 47, Issue 7–8, pp 293–305 | Cite as

Performances des codes en treillis sur le canal gaussien

  • Hélio MagalhÃes De Oliveira
  • Gérard Battail
Article

Résumé

On établit une borne supérieure de la probabilité ďerreur ďun code défini par un treillis de points combiné à la modulation ďamplitude en quadrature, sur le canal à bruit additif gaussien et blanc. Cette borne dépend ďun facteur de mérite du treillis et peut être facilement mise sous la forme exponentielle de Chernoff. Une intéressante borne inférieure est obtenue par un raisonnement similaire. On examine aussi ľestimation du débit ďinformation basée sur ľapproximation continue de la puissance moyenne normalisée è deux dimensions. On suggère de ľaméliorer en utilisant ľidée ďempilement de sphères. Des exemples ďévaluation des performances sont donnés pour quelques treillis. On présente finalement des bornes inférieure et supérieure des meilleurs gains de codage fondamentaux par dimension (déduits de la densité et de ľépaisseur) pour un nombre de dimensions arbitraitement grand. On montre dans ľannexe que les codes en treillis, comme ceux ďUngerboeck, n’ont pas ďeffet sur la forme du spectre de puissance des signaux.

Mots clés

Codage treillis Canal gaussien Probabilité erreur Jeu signal Espace multidimensionnel Modulation quadrature 

Performance of lattice codes over the Gaussian channel

Abstract

We derive an upper bound on the error probability of lattice codes combined with Quadrature Amplitude Modulation (qam) over the additive white Gaussian noise channel. This bound depends on a lattice figure of merit and is readily put in exponential form by using Chernoff bound. An interesting lower bound is derived by a similar reasoning. We also examine the estimation of the average information rate based upon the continuous approximation of the average power normalized to two dimensions, and suggest to improve it by using the sphere packing idea. Examples of performance evaluation are given for a few lattices. Finally, we present upper and lower bounds on the best fundamental coding gains per dimension (due to both density and thickness) for an arbitrarily large number of dimensions. It is shown in the Appendix that, as the Ungerboeck codes, the lattice codes do not shape the signal power spectrum.

Key words

Lattice coding Gaussian channel Error probability Signal set Multidimensional space Quadrature modulation 

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Hélio MagalhÃes De Oliveira
    • 1
  • Gérard Battail
    • 2
  1. 1.Department of electronics and systems, communication research group — CODECFederal University of PernambucoRecifeBrazil
  2. 2.Département communicationsEcole nationale supérieure des télécommunications (Telecom Paris)Paris Cedex 13France

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