On the construction of perfect codes from HEX signal constellations

Recently, minimum and non-minimum delay perfect codes were proposed for any channel of dimension n. Their construction appears in the literature as a subset of cyclic division algebras over Q(zeta(3)) only for the dimension n = 2(s)n(1), where s is an element of {0,1}, n(1) is odd and the signal constellations are isomorphic to Z[zeta(3)](n) In this work, we propose an innovative methodology to extend the construction of minimum and non-minimum delay perfect codes as a subset of cyclic division algebras over Q(zeta(3)), where the signal constellations are isomorphic to the hexagonal A(2)(n)-rotated lattice, for any channel of any dimension n such that gcd(n,3) = 1. (C) 2012 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Some Initial Conditions for Disposed Satellites of the Systems GPS and Galileo Constellations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the Optimality of Finite Constellations from Algebraic Lattices

A construction technique of finite point constellations in n-dimensional spaces from ideals in rings of algebraic integers is described. An algorithm is presented to find constellations with minimum average energy from a given lattice. For comparison, a numerical table of lattice constellations and group codes is computed for spaces of dimension two, three, and four. © 2001.

Lattice constellations and codes from quadratic number fields

We propose new classes of linear codes over integer rings of quadratic extensions of Q, the field of rational numbers. The codes are considered with respect to a Mannheim metric, which is a Manhattan metric modulo a two-dimensional (2-D) grid. In particular, codes over Gaussian integers and Eisenstein-Jacobi integers are extensively studied. Decoding algorithms are proposed for these codes when up to two coordinates of a transmitted code vector are affected by errors of arbitrary Mannheim weight. Moreover, we show that the proposed codes are maximum-distance separable (MDS), with respect to the Hamming distance. The practical interest in such Mannheim-metric codes is their use in coded modulation schemes based on quadrature amplitude modulation (QAM)-type constellations, for which neither the Hamming nor the Lee metric is appropriate.

Optimization of satellite constellations in the moon

Nowadays, we return to live a period of lunar exploration. China, Japan and India heavily invest in missions to the moon, and then try to implement manned bases on this satellite. These bases must be installed in polar regions due to the apparent existence of water. Therefore, the study of the feasibility of satellite constellations for navigation, control and communication recovers importance. The Moon's gravitational potential and resonant movements due to the proximity to Earth as the Kozai-Lidov resonance, must be considered in addition to other perturbations of lesser magnitude. The usual satellite constellations provide, as a basic feature, continuous and global coverage of the Earth. With this goal, they are designed for the smallest number of objects possible to perform a specific task and this amount is directly related to the altitude of the orbits and visual abilities of the members of the constellation. However the problem is different when the area to be covered is reduced to a given zone. The required number of space objects can be reduced. Furthermore, depending on the mission requirements it may be not necessary to provide continuous coverage. Taking into account the possibility of setting up a constellation that covers a specific region of the Moon on a non-continuous base, in this study we seek a criterion of optimization related to the time between visits. The propagation of the orbits of objects in the constellation in conjunction with the coverage constraints, provide information on the periods of time in which points of the surface are covered by a satellite, and time intervals in which they are not. So we minimize the time between visits considering several sets of possible constellations and using genetic algorithms.

CIGALA: Challenging the solar maximum in Brazil with PolaRxS

The upcoming solar maximum, which is expected to reach its peak around May 2013, occurs at a time when our reliance on high-precision GNSS has reached unprecedented proportions. The perturbations of the ionosphere caused by increased solar activity pose a major threat to these applications. This is particularly true in equatorial regions where high exposure to solar-induced disturbances is coupled with explosive growth of precise GNSS applications. Along with the various types of solar-induced ionospheric disturbances, strong scintillations are amongst the most challenging, causing phase measurement errors up to full losses of lock for several satellites. Brazil, which heavily relies on high-precision GNSS, is one of the most affected regions due notably to the proximity to the southern crest of the ionospheric equatorial anomaly and to the South Atlantic Magnetic Anomaly. In the framework of the CIGALA project, we developed the PolaRxS™, a GNSS receiver dedicated to the monitoring of ionospheric scintillation indices not only in the GPS L1 band but for all operational and upcoming constellations and frequency bands. A network of these receivers was deployed across the whole Brazilian territory in order to first investigate and secondly to mitigate the impact of scintillation on the different signals, ensuring high precision GNSS availability and integrity in the area. This paper reports on the validation of the PolaRxS™ receiver as an ionospheric scintillation monitor and the first results of the analysis of the data collected with the CIGALA network.

Construction of perfect space-time codes

In this work, we propose an innovative methodology to extend the construction of minimum and non-minimum delay perfect codes as a subset of cyclic division algebras over ℚ(ζ3), where the signal constellations are isomorphic to the hexagonal An 2 -rotated lattice, for any channel of any dimension n such that gcd{n, 3) = 1.

Construção de Códigos Espaço-temporais de Treliça via Partição de Reticulados

Pós-graduação em Engenharia Elétrica - FEIS

Dinâmica ressonante de alguns satélites artificiais terrestres no sistema Terra-Lua-Sol

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Constelações ciclotômicas

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A contribuition to the study of channel coding in wireless communication systems

Pós-graduação em Engenharia Elétrica - FEIS

Lattices from subfields of Q (xi n)

In this paper we present a method for evaluating the center density of algebraic lattices from subfields of Q(xi n), where n is a positive integer. This method allows to reproduce rotated versions of dense lattices in some dimensions. Constellations on algebraic lattices with high packing density have been proposed for use in communications in Gaussian channels and also in Rayleigh fading channels in case they have high diversity.