Curves on torus layers and coding for continuous alphabet sources

In this paper we consider the problem of transmitting a continuous alphabet discrete-time source over an AWGN channel. The design of good curves for this purpose relies on geometrical properties of spherical codes and projections of $N$-dimensional lattices. We propose a constructive scheme based on a set of curves on the surface of a 2N-dimensional sphere and present comparisons with some previous works.Comment: 5 pages, 4 figures. Accepted for presentation at 2012 IEEE International Symposium on Information Theory (ISIT). 2th version: typos corrected. 3rd version: some typos corrected, a footnote added in Section III B, a comment added in the beggining of Section V and Theorem I adde

Does Geometric Coupling Generates Resonances?

Geometrical coupling in a co-dimensional one Randall-Sundrum scenario (RS) is used to study resonances of $p-$form fields. The resonances are calculated using the transfer matrix method. The model studied consider the standard RS with delta-like branes, and branes generated by kinks and domain-wall as well. The parameters are changed to control the thickness of the smooth brane. With this a very interesting pattern is found for the resonances. The geometrical coupling does not generate resonances for the reduced $p-$form in all cases considered.Comment: 10 pages, 10 figure

Constructive spherical codes on layers of flat tori

A new class of spherical codes is constructed by selecting a finite subset of flat tori from a foliation of the unit sphere S^{2L-1} of R^{2L} and designing a structured codebook on each torus layer. The resulting spherical code can be the image of a lattice restricted to a specific hyperbox in R^L in each layer. Group structure and homogeneity, useful for efficient storage and decoding, are inherited from the underlying lattice codebook. A systematic method for constructing such codes are presented and, as an example, the Leech lattice is used to construct a spherical code in R^{48}. Upper and lower bounds on the performance, the asymptotic packing density and a method for decoding are derived.Comment: 9 pages, 5 figures, submitted to IEEE Transactions on Information Theor