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.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

Geometric phase and periodic orbits of the equal-mass, planar three-body problem with vanishing angular momentum

Geometric phase can explain the rotation of a dynamical system independent of angular momentum. The canonical example of such is a cat (a non-rigid body with an inbuilt control system), falling from an inverted position, being able to re-orient itself with negligible total angular momentum so as to land on its feet. The system of three bodies moving under mutual gravitation is similarly non-rigid, capable of changing size and shape under the dynamics of that force. Using coordinates that reduce by translations and rotations and simultaneously regularise all binary collisions, which separate shape dynamics from rotational dynamics, we show how certain discrete symmetries (including both reversing and non-reversing symmetries of the equations of motion) can force the geometric phase of motion periodic to vanish. This result is illustrated with periodic orbits discovered in a numerical survey, many of which are heretofore unknown, and the findings of this survey are discussed in detail, including stability, geometric phase, and classification of orbits

Geometric phase and periodic orbits of the equal-mass, planar three-body problem with vanishing angular momentum

Geometric phase can explain the rotation of a dynamical system independent of angular momentum. The canonical example of such is a cat (a non-rigid body with an inbuilt control system), falling from an inverted position, being able to re-orient itself with negligible total angular momentum so as to land on its feet. The system of three bodies moving under mutual gravitation is similarly non-rigid, capable of changing size and shape under the dynamics of that force. Using coordinates that reduce by translations and rotations and simultaneously regularise all binary collisions, which separate shape dynamics from rotational dynamics, we show how certain discrete symmetries (including both reversing and non-reversing symmetries of the equations of motion) can force the geometric phase of motion periodic to vanish. This result is illustrated with periodic orbits discovered in a numerical survey, many of which are heretofore unknown, and the findings of this survey are discussed in detail, including stability, geometric phase, and classification of orbits

On sequences of projections of the cubic lattice

In this paper we study sequences of lattices which are, up to similarity, projections of $\mathbb{Z}^{n+1}$ onto a hyperplane $\bm{v}^{\perp}$, with $\bm{v} \in \mathbb{Z}^{n+1}$ and converge to a target lattice $\Lambda$ which is equivalent to an integer lattice. We show a sufficient condition to construct sequences converging at rate $O(1/ |\bm{v}|^{2/n})$ and exhibit explicit constructions for some important families of lattices.Comment: 16 pages, 5 figure

Image Transmission: Analog or Digital?

Trátase dun resumo estendido da ponencia[Abstract] Evaluation and comparison of analog and digital wireless transmission systems.Xunta de Galicia; ED431C 2016-045Xunta de Galicia; , ED341D R2016/012Xunta de Galicia; ED431G/01Agencia Estatal de Investigacion de España; TEC2015-69648-REDC,Agencia Estatal de Investigacion de España; TEC2016-75067-C4-1-RMinisterio de Economía y Competitividad; BES-2014-069772

Soft Processing Techniques for Quantum Key Distribution Applications

This thesis deals with soft-information based information reconciliation and data sifting for Quantum Key Distribution (QKD). A novel composite channel model for QKD is identified, which includes both a hard output quantum channel and a soft output classic channel. The Log-Likelihood Ratios, - also called soft-metrics - derived from the two channels are jointly processed at the receiver, exploiting capacity achieving soft-metric based iteratively decoded block codes. The performance of the proposed mixed-soft-metric algorithms are studied via simulations as a function of the system parameters. The core ideas of the thesis are employing Forward Error Correction (FEC) coding as opposed to two-way communication for information reconciliation in QKD schemes, exploiting all the available information for data processing at the receiver including information available from the quantum channel, since optimized use of this information can lead to significant performance improvement, and providing a security versus secret-key rate trade-off to the end-user within the context of QKD system