We consider two codes based on dynamical systems, for transmitting information from a continuous alphabet, discrete-time source over Gaussian channel. The first code, homogeneous spherical is generated by the linear system s/spl dot/=As, with A square skew-symmetric matrix. second code shift map s/sub n/=b/sub n/s/sub n-1/(mod 1). performance of each these determined geometry its locus or signal set, specifically, arc length and minimum distance, suitably defined. show that analyses systems...

The index coding problem aims to optimise broadcast communication by taking advantage of receiver-side information improve transmission efficiency. In this letter, we explore the application Construction $\pi_A$ lattices coding. We introduce a scheme, named \textit{CRT lattice coding}, using over $\mathbb{Z}$ address problem. It is derived an upper bound for side gain CRT code and conditions uniformity gain. efficiency approach shown through theoretical analysis design examples.

Quadrature amplitude modulation (QAM)-like signal sets are considered in this paper as coset constellations placed on regular graphs surfaces known flat tori. Such can be related to spherical, block, and trellis codes may viewed geometrically uniform (GU) the graph metric a sense that extends concept introduced by Forney . Homogeneous of any order then labeled cyclic group, induced translations Euclidean plane. We construct classes perfect square including Lee spaces, hexagonal triangular...

The Fisher–Rao distance is a measure of dissimilarity between probability distributions, which, under certain regularity conditions the statistical model, up to scaling factor unique Riemannian metric invariant Markov morphisms. It related Shannon entropy and has been used enlarge perspective analysis in wide variety domains such as image processing, radar systems, morphological classification. Here, we approach this considered model normal multivariate for which there not an explicit...

In this work we present constructions of algebraic lattices in Euclidean space with optimal center density dimensions 2, 3, 4, 6, 8 and 12, which are rotated versions the Λn, for n = 2,3,4,6,8 K12. These constructed through twisted canonical homomorphism via ideals a ring integers. Mathematical subject classification: 18B35, 94A15, 20H10.

Twisted curves in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="bold upper R Superscript m"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi mathvariant="bold">R</mml:mi> </mml:mrow> <mml:mi>m</mml:mi> </mml:msup> <mml:annotation encoding="application/x-tex">{{\mathbf {R}}^m}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are those which have independent derivatives up to order alttext="m">...

The Fisher information matrix induces a metric on parametric spaces of families probability density functions. We analyse here the family normal distributions showing how hyperbolic geometry arises naturally from metric.

Information geometry is approached here by considering the statistical model of multivariate normal distributions as a Riemannian manifold with natural metric provided Fisher information matrix. Explicit forms for Fisher-Rao distance associated to this and geodesics general distribution models are usually very hard determine. In case lower upper bounds have been derived. We approach some these introduce new one discussing their tightness in specific cases.

A new class of spherical codes is constructed by selecting a finite subset flat tori that foliate the unit sphere S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2L-1</sup> sub R xmlns:xlink="http://www.w3.org/1999/xlink">2L</sup> and constructing structured codebook on each torus in subset. The image lattice restricted to specific hyperbox xmlns:xlink="http://www.w3.org/1999/xlink">L</sup> . Group structure homogeneity, useful for efficient...

This work presents an extension of the Construction $\pi_A$ lattices proposed in \cite{huang2017construction}, to Hurwitz quaternion integers. construction is provided by using isomorphism from a version Chinese remainder theorem applied maximal orders contrast natural prior works. Exploiting this map, we analyze performance resulting multilevel lattice codes, highlight via computer simulations their notably reduced computational complexity multistage decoding. Moreover it shown that...

A new class of spherical codes is constructed by selecting a finite subset flat tori from foliation the unit sphere S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2L-1</sup> ⊂ R xmlns:xlink="http://www.w3.org/1999/xlink">2L</sup> and designing structured codebook on each torus layer. The resulting code can be image lattice restricted to specific box in xmlns:xlink="http://www.w3.org/1999/xlink">L</sup> Group structure homogeneity, useful for...

A cylinder anchored at two distinct points of the lattice Z <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> is called a strut if its interior does not contain point. We address problem constructing struts maximal radius in . Our main result general construction technique, which we call lifting construction, produces sequence that are optimal limit. also tighten previous ours - an achievable lower bound on volume strut. The motivated by...