Construction of lattices and applications in Information Theory

• Grant number: 14/14449-2
• Support Opportunities: Regular Research Grants
• Start date: November 01, 2014
• End date: October 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Agnaldo José Ferrari
• Grantee: Agnaldo José Ferrari
• Host Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil
• Associated researchers: Antonio Aparecido de Andrade

Abstract

The Algebraic number theory has played an important role in building codes and algebraic lattices. Find algebraic lattices via numbers fields with maximum diversity and minimum product distance has been the subject of study in recent years. Algebraic lattices are those obtained using the ring of integers of a number field and ideal lattices are algebraic lattices endowed with a trace form. The theory of ideal lattices has shown to be useful in information theory. Ideal lattices with high packing density have been studied as an alternative approach for signal transmission over Gaussian channel, which is a communication channel of the type AWGN ( Additive White Gaussian Noise ), where attenuations and delays of signal propagation predominate. Ideal lattices with high diversity and minimum product distance are interesting for signal transmission over Rayleigh fading channel, which is a communication channel that has as main characteristic the multipath propagation. Lattices obtained via quotients rings, which were initially introduced as tools for lattice-based cryptography, has been little explored in relation to construction of known lattices in the literature and also in relation to other applications. This research project aims to: (i) the construction of both ideal lattices for the Gaussian channel and for the Rayleigh fading channel, which perform better than the constructions known in the literature as well as explore new constructions. (ii) explore theoretical and applied field lattices obtained via quotients rings. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

FERRARI, AGNALDO JOSE; DE ANDRADE, ANTONIO APARECIDO. Algebraic lattices via polynomial rings. COMPUTATIONAL & APPLIED MATHEMATICS, v. 38, n. 4, DEC 2019. (13/25977-7, 14/14449-2)

STRAPASSON, JOAO ELOIR; FERRARI, AGNALDO JOSE; JORGE, GRASIELE CRISTIANE; COSTA, SUELI IRENE RODRIGUES. Algebraic constructions of rotated unimodular lattices and direct sum of Barnes-Wall lattices. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, v. 20, n. 3, p. 23-pg., 2021-03-01. (13/25977-7, 15/17167-0, 14/14449-2)

FERRARI, AGNALDO JOSE; DE ANDRADE, ANTONIO APARECIDO. Algebraic lattices via polynomial rings. COMPUTATIONAL & APPLIED MATHEMATICS, v. 38, n. 4, p. 18-pg., 2019-12-01. (13/25977-7, 14/14449-2)