—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)
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 from a foliation of the unit sphere S 2L−1 ⊂ 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… (More)
—A cylinder anchored at two distinct points of a lattice Λ ⊂ R n is called a strut if its interior does not contain a lattice point. We address the problem of constructing struts of maximal radius in a general number of dimensions. Our main contribution is a general construction technique, which we call the lifting construction. The lifting construction,… (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)
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)
It is shown that, given any (n − 1)-dimensional lattice Λ, there is a vector v ∈ Z n such that the orthogonal projection of Z n onto v ⊥ is, up to a similarity, arbitrarily close to Λ. 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 .