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Construction of lattices and applications in Information Theory

Grant number: 14/14449-2
Support type:Regular Research Grants
Duration: November 01, 2014 - October 31, 2016
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal researcher:Agnaldo José Ferrari
Grantee:Agnaldo José Ferrari
Home Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil
Assoc. 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. Web of Science Citations: 0.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.