Lattices and Spherical Codes

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

doi:10.1007/978-3-319-67882-5_5

Lattices and Spherical Codes

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

^*Corresponding author for this work

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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 language	English
Title of host publication	SpringerBriefs in Mathematics
Publisher	Springer Science and Business Media B.V.
Pages	73-92
Number of pages	20
DOIs	https://doi.org/10.1007/978-3-319-67882-5_5
Publication status	Published - 2017

Publication series

Name	SpringerBriefs in Mathematics
ISSN (Print)	2191-8198
ISSN (Electronic)	2191-8201

Bibliographical note

Publisher Copyright:
© 2017, The Author(s).

ASJC Scopus subject areas

General Mathematics

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10.1007/978-3-319-67882-5_5

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AU - Costa, Sueli I.R.

AU - Oggier, Frédérique

AU - Campello, Antonio

AU - Belfiore, Jean Claude

AU - Viterbo, Emanuele

PY - 2017

Y1 - 2017

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BT - SpringerBriefs in Mathematics

PB - Springer Science and Business Media B.V.

ER -

Lattices and Spherical Codes

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