arXiv subjects

Sueli I. R. Costa

Publications and source records attributed to Sueli I. R. Costa.

23 records · Page 2Linked to original sources

arXiv2012

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.

cs.IT↗

arXiv2012

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.

cs.IT↗

arXiv2012

Decoding q-ary lattices in the Lee metric

q-ary lattices can be obtained from q-ary codes using the so-called Construction A. We investigate these lattices in the Lee metric and show how their decoding process can be related to the associated codes. For prime q we derive a Lee sphere decoding algorithm for q-ary lattices, present a brief discussion on its complexity and some comparisons with the classic sphere decoding.

cs.IT↗

arXiv2011

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.

cs.IT↗

arXiv2010

A Note on Projecting the Cubic Lattice

It is shown that, given any (n-1)-dimensional lattice L, there is a vector v in Z^n such that the projection of Z^n onto v^perp is arbitrarily close to L. The problem arises in attempting to find the largest cylinder anchored at two points of Z^n and containing no other points of Z^n.

math.NT↗