SIGNAL CONSTELLATIONS FROM LATTICES IN QUATERNION ALGEBRAS
EDUARDO BRANDANI DA SILVA *
Department of Mathematics, Universidade Estadual de Maring´a - UEM, PR Brazil.
EDSON DONIZETE DE CARVALHO
Department of Mathematics, Unesp at Ilha Solteira, SP Brazil
ANTONIO APARECIDO ANDRADE
Department of Mathematics, Unesp at S˜ao Jos´e do Rio Preto, SP Brazil.
*Author to whom correspondence should be addressed.
Signal constellations are fundamental ingredients in communication theory. In the current work is presented an efficient tool for the design of signals constellations obtained from some compact surfaces originated from Fuchsian groups of the first kind associated to the fundamental polygon of the hyperbolic auto-dual tessellations. The design criteria is related to properties of underlying quotient of lattices by sublattices in quaternion algebras. For it, we propose a theoretical criterion for the construction of sublattices from lattices in quaternion algebras, and also a method to compute the index associated to the quotient of a lattice by a sublattice.
Keywords: Communication systems, fuchsian groups, quaternion algebras, hyperbolic geometry, coding theory, signal constellations