Algebraic lattices via polynomial rings
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/s40314-019-0948-8 http://hdl.handle.net/11449/197998 |
Resumo: | Signal constellations having lattice structure have been studied as meaningful means for signal transmission over Gaussian channel. Usually the problem of finding good signal constellations for a Gaussian channel is associated with the search for lattices with high packing density, where in general the packing density is usually hard to estimate. The aim of this paper was to illustrate the fact that the polynomial ring Z[x] can produce lattices with maximum achievable center density, where Z is the ring of rational integers. Essentially, the method consists of constructing a generator matrix from a quotient ring of Z[x]. |
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Repositório Institucional da UNESP |
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2946 |
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Algebraic lattices via polynomial ringsCenter densityGalois ringLatticePacking densitySignal constellations having lattice structure have been studied as meaningful means for signal transmission over Gaussian channel. Usually the problem of finding good signal constellations for a Gaussian channel is associated with the search for lattices with high packing density, where in general the packing density is usually hard to estimate. The aim of this paper was to illustrate the fact that the polynomial ring Z[x] can produce lattices with maximum achievable center density, where Z is the ring of rational integers. Essentially, the method consists of constructing a generator matrix from a quotient ring of Z[x].Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)School of Sciences São Paulo State University (Unesp)Department of Mathematics São Paulo State University (Unesp)School of Sciences São Paulo State University (Unesp)Department of Mathematics São Paulo State University (Unesp)FAPESP: 2013/25977-7FAPESP: 2014/14449-2Universidade Estadual Paulista (Unesp)Ferrari, Agnaldo José [UNESP]de Andrade, Antonio Aparecido [UNESP]2020-12-12T00:56:08Z2020-12-12T00:56:08Z2019-12-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1007/s40314-019-0948-8Computational and Applied Mathematics, v. 38, n. 4, 2019.1807-03022238-3603http://hdl.handle.net/11449/19799810.1007/s40314-019-0948-82-s2.0-85073244623Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengComputational and Applied Mathematicsinfo:eu-repo/semantics/openAccess2021-10-23T07:59:07Zoai:repositorio.unesp.br:11449/197998Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T22:02:28.481216Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Algebraic lattices via polynomial rings |
title |
Algebraic lattices via polynomial rings |
spellingShingle |
Algebraic lattices via polynomial rings Ferrari, Agnaldo José [UNESP] Center density Galois ring Lattice Packing density |
title_short |
Algebraic lattices via polynomial rings |
title_full |
Algebraic lattices via polynomial rings |
title_fullStr |
Algebraic lattices via polynomial rings |
title_full_unstemmed |
Algebraic lattices via polynomial rings |
title_sort |
Algebraic lattices via polynomial rings |
author |
Ferrari, Agnaldo José [UNESP] |
author_facet |
Ferrari, Agnaldo José [UNESP] de Andrade, Antonio Aparecido [UNESP] |
author_role |
author |
author2 |
de Andrade, Antonio Aparecido [UNESP] |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Ferrari, Agnaldo José [UNESP] de Andrade, Antonio Aparecido [UNESP] |
dc.subject.por.fl_str_mv |
Center density Galois ring Lattice Packing density |
topic |
Center density Galois ring Lattice Packing density |
description |
Signal constellations having lattice structure have been studied as meaningful means for signal transmission over Gaussian channel. Usually the problem of finding good signal constellations for a Gaussian channel is associated with the search for lattices with high packing density, where in general the packing density is usually hard to estimate. The aim of this paper was to illustrate the fact that the polynomial ring Z[x] can produce lattices with maximum achievable center density, where Z is the ring of rational integers. Essentially, the method consists of constructing a generator matrix from a quotient ring of Z[x]. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-12-01 2020-12-12T00:56:08Z 2020-12-12T00:56:08Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1007/s40314-019-0948-8 Computational and Applied Mathematics, v. 38, n. 4, 2019. 1807-0302 2238-3603 http://hdl.handle.net/11449/197998 10.1007/s40314-019-0948-8 2-s2.0-85073244623 |
url |
http://dx.doi.org/10.1007/s40314-019-0948-8 http://hdl.handle.net/11449/197998 |
identifier_str_mv |
Computational and Applied Mathematics, v. 38, n. 4, 2019. 1807-0302 2238-3603 10.1007/s40314-019-0948-8 2-s2.0-85073244623 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Computational and Applied Mathematics |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808129385716252672 |