Lattices and Spherical Codes

Sueli I.R. Costa, Frédérique Oggier, Antonio Campello, Jean Claude Belfiore, Emanuele Viterbo

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Abstract

Lattices in ℝn with sublattices which have an orthogonal basis are associated with spherical codes in ℝ2n generated by a finite commutative group of orthogonal matrices. They also can be used to construct homogeneous spherical curves for transmitting a continuous alphabet source over an AWGN channel. In both cases, the performance of the decoding process is related to the packing density of the lattices (see (2.13 )). In the continuous case, the packing density of these curves relies on the search for projection lattices with good packing density. We present here a survey on this topic mainly based on [18, 31, 96, 105].

Original languageEnglish
Title of host publicationLattices Applied to Coding for Reliable and Secure Communications
EditorsSueli I.R. Costa, Frederique Oggier, Antonio Campello, Jean-Claude Belfiore, Emanuele Viterbo
Place of PublicationCham Switzerland
PublisherSpringer
Chapter5
Pages73-92
Number of pages20
Edition1st
ISBN (Electronic)9783319678825
ISBN (Print)9783319678818
DOIs
Publication statusPublished - 2017

Publication series

NameSpringerBriefs in Mathematics
PublisherSpringer
ISSN (Print)2191-8198
ISSN (Electronic)2191-8201

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