Constructions of Dense Lattices of Full Diversity

Author(s)

A. A. ANDRADE ^[1] ; A. J. FERRARI ^[2] ; J. C. INTERLANDO ^[3] ; R.R. ARAUJO ^[4]

Affiliation

^[1] Universidade Estadual Paulista “Júlio de Mesquita Filho”. Instituto de Biociências, Letras e Ciências Exatas. Departamento de Matemática - Brasil

^[2] Universidade Estadual Paulista “Júlio de Mesquita Filho”. Faculdade de Ciências. Departamento de Matemática - Brasil

^[3] San Diego State University. Department of Mathemtaics & Statistics - Estados Unidos

^[4] Instituto Federal de São Paulo - Brasil

• Document type: Journal article
• Source: TEMA (São Carlos); v. 21, n. 2, p. 299-311, 2020-08-03.

Abstract

ABSTRACT A lattice construction using ℤ-submodules of rings of integers of number fields is presented. The construction yields rotated versions of the laminated lattices Λ n f o r n = 2 , 3 , 4 , 5 , 6, which are the densest lattices in their respective dimensions. The sphere packing density of a lattice is a function of its packing radius, which in turn can be directly calculated from the minimum squared Euclidean norm of the lattice. Norms in a lattice that is realized by a totally real number field can be calculated by the trace form of the field restricted to its ring of integers. Thus, in the present work, we also present the trace form of the maximal real subfield of a cyclotomic field. Our focus is on totally real number fields since their associated lattices have full diversity. Along with high packing density, the full diversity feature is desirable in lattices that are used for signal transmission over both Gaussian and Rayleigh fading channels. (AU)

• FAPESP's process: 13/25977-7 - Security and reliability of Information: theory and practice
• Grantee: Marcelo Firer
• Support Opportunities: Research Projects - Thematic Grants