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We consider two codes based on dynamical systems, for transmitting information from a continuous alphabet, discrete-time source over a Gaussian channel. The first code, a homogeneous spherical code, is generated by the linear dynamical system s/spl dot/=As, with A a square skew-symmetric matrix. The second code is generated by the shift map s/sub n/=b/sub(More)
This paper explores the use of elements of Diierential Geometry to control the manipulation of the deformable model proposed by Terzopoulos et al. 8] for animating deformable objects. Particularly, we are interested on the animation of deformable panels without stretching (area invariant), such as clothes and papers. Based on our analysis we could generate(More)
We investigate perfect codes in Z n in the p metric. Upper bounds for the packing radius r of a linear perfect code in terms of the metric parameter p and the dimension n are derived. For p = 2 and n = 2, 3, we determine all radii for which there exist linear perfect codes. The non-existence results for codes in Z n presented here imply non-existence(More)
Quadrature amplitude modulation (QAM)-like signal sets are considered in this paper as coset constellations placed on regular graphs on surfaces known as flat tori. Such signal sets can be related to spherical, block, and trellis codes and may be viewed as geometrically uniform (GU) in the graph metric in a sense that extends the concept introduced by(More)
This paper is a strongly geometrical approach to the Fisher distance, which is a measure of dissimilarity between two probability distribution functions. The Fisher distance, as well as other divergence measures, are also used in many applications to establish a proper data average. The main purpose is to widen the range of possible interpretations and(More)
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(More)
A method for finding an optimum n-dimensional commutative group code of a given order M is presented. The approach explores the structure of lattices related to these codes and provides a significant reduction in the number of non-isometric cases to be analyzed. The classical factorization of matrices into Hermite and Smith normal forms and also basis(More)
A new class of spherical codes is constructed by selecting a finite subset of flat tori that foliate the unit sphere S<sup>2L&#x2212;1</sup> &#x2282; &#x211D;<sup>2L</sup> and constructing a structured codebook on each torus in the finite subset. The codebook on each torus is the image of a lattice restricted to a specific hyperbox in &#x211D;<sup>L</sup>.(More)
A new class of spherical codes is constructed by selecting a finite subset of flat tori from a foliation of the unit sphere S<sup>2L-1</sup> &#x2282; R<sup>2L</sup> and designing a structured codebook on each torus layer. The resulting spherical code can be the image of a lattice restricted to a specific box in R<sup>L</sup> in each layer. Group structure(More)