Algebraic lattices via polynomial rings
| Autor: | Antonio Aparecido de Andrade, Agnaldo José Ferrari |
|---|---|
| Přispěvatelé: | Universidade Estadual Paulista (Unesp) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Physics
Ring (mathematics) Applied Mathematics Polynomial ring Packing density 010102 general mathematics Center (category theory) Lattice Center density 01 natural sciences Signal Combinatorics Computational Mathematics Sphere packing 0103 physical sciences 010307 mathematical physics Generator matrix 0101 mathematics Algebraic number Galois ring Quotient ring |
| Zdroj: | Scopus Repositório Institucional da UNESP Universidade Estadual Paulista (UNESP) instacron:UNESP |
| Popis: | 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 $$\mathbb {Z}[x]$$ can produce lattices with maximum achievable center density, where $$\mathbb {Z}$$ is the ring of rational integers. Essentially, the method consists of constructing a generator matrix from a quotient ring of $$\mathbb {Z}[x]$$ . |
| Databáze: | OpenAIRE |
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