Arithmetic fuchsian groups identified in quaternion orders for the construction of signal constellations / Grupos fuchsianos aritmeticos identificados em ordens dos quaternios para construção de constelações de sinais

AUTOR(ES)

Vandenberg Lopes Vieira

DATA DE PUBLICAÇÃO

2007

RESUMO

Within the context of digital communications system in homogeneous space in particular, in hyperbolic spaces, it is necessary to establish systematic procedure for the construction of lattices O ; as the basic entity for construction of eometrically uniforms signal constellations. By this procedure we identify the algebraic and geometric structures to construct geometrically uniforms codes in homogeneous spaces. We propose, from lattices, the construction of arithmetic fuchsian groups ¡p obtained by hyperbolic tessellations {p; q}, derived from division quaternion algebras A over numbers fields K. We generalize the process of identification of these groups in quaternion orders (hyperbolic lattices), which are associated with geometrically uniforms signal constellations, proceeding from discrete groups. This procedure allows us to realize the labelling of the signals belonging to such constellations by elements of an algebraic structure

ASSUNTO(S)

mobius transformations algebra algebra quaterion order riemann surfaces geometrically uniform signal constelattion fuchsian group superficies de transformações de quaternios mobius riemann quaternions quotient surface

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