Construção e análise de códigos esféricos com boas taxas binárias
DOI:
https://doi.org/10.5540/tema.2013.014.01.0013Abstract
Neste trabalho consideramos a distribuição de um conjunto discreto de pontos sobre a superfície de uma esfera euclidiana unitária, com o propósito de construir códigos esféricos para o canal Gaussiano. Apresentamos famílias de códigos esféricos estruturados, que podem ser construídas em tempo linear para dimensões pares e superam, para alguns parâmetros, o limitante inferior de Shannon para a taxa binária de informação.References
M. Berger, and B. Gostiaux, "Differential Geometry: Manifolds, Curves and Surfaces''. Springer-Verlag, Berlin, 1988.
J.H. Conway, N.J.A. Sloane, "Sphere packings, lattices and groups'', Springer Verlag, GMW 290, 2003.
S. I. R. Costa, M.M. Alves, E. Agustini, and R. Palazzo, "Graphs, tesselations and perfect codes on flat tori'', IEEE Transactions on Information Theory, vol. 50, pp. 2363-2377, Oct. 2004.
T. Ericson, V. Zinoviev, "Codes on Euclidean spheres'', North-Holland, Amsterdam, 2001.
G. Lachaud, J. Stern, "Polynomial-time construction of codes. II Spherical codes and the kissing number of spheres'', IEEE Trans. Inform. Theory 40, 1994, n 4, 1140 - 1146.
C. Torezzan, "Códigos esféricos em toros planares'', Tese de doutorado, IMECC-Unicamp, 2009.
C. Torezzan, S. I. R. Costa, "Linear time constructive spherical codes with good binary rates'', Submetido.
C. Torezzan, S. I. R. Costa, & V. A. Vaishampayan, "Spherical codes on torus layers'', International Symposium on Information Theory, Seul, Coreia, 2009.
P. Solé, J.C. Belfiore,"Constructive spherical codes near the Shannon bound'', The Seventh International Workshop on Coding and Cryptography 2011, Paris, França.
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