Algebraic lattices via polynomial rings

• Autor(a) principal: Ferrari, Agnaldo José [UNESP]
• Data de Publicação: 2019
• Outros Autores: de Andrade, Antonio Aparecido [UNESP]
• 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
• topic: Center density; Galois ring; Lattice; Packing density

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].