83 research outputs found
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
-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
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
An Upper Bound for Signal Transmission Error Probability in Hyperbolic Spaces
We introduce and discuss the concept of Gaussian probability density function
(pdf) for the n-dimensional hyperbolic space which has been proposed as an
environment for coding and decoding signals. An upper bound for the error
probability of signal transmission associated with the hyperbolic distance is
established. The pdf and the upper bound were developed using Poincare models
for the hyperbolic spaces
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