7,830 research outputs found
Distributed Lossy Averaging
An information theoretic formulation of the distributed averaging problem
previously studied in computer science and control is presented. We assume a
network with m nodes each observing a WGN source. The nodes communicate and
perform local processing with the goal of computing the average of the sources
to within a prescribed mean squared error distortion. The network rate
distortion function R^*(D) for a 2-node network with correlated Gaussian
sources is established. A general cutset lower bound on R^*(D) is established
and shown to be achievable to within a factor of 2 via a centralized protocol
over a star network. A lower bound on the network rate distortion function for
distributed weighted-sum protocols, which is larger in order than the cutset
bound by a factor of log m is established. An upper bound on the network rate
distortion function for gossip-base weighted-sum protocols, which is only log
log m larger in order than the lower bound for a complete graph network, is
established. The results suggest that using distributed protocols results in a
factor of log m increase in order relative to centralized protocols.Comment: 25 pages, 1 figur
The effect of short ray trajectories on the scattering statistics of wave chaotic systems
In many situations, the statistical properties of wave systems with chaotic
classical limits are well-described by random matrix theory. However,
applications of random matrix theory to scattering problems require
introduction of system specific information into the statistical model, such as
the introduction of the average scattering matrix in the Poisson kernel. Here
it is shown that the average impedance matrix, which also characterizes the
system-specific properties, can be expressed in terms of classical trajectories
that travel between ports and thus can be calculated semiclassically.
Theoretical results are compared with numerical solutions for a model
wave-chaotic system
Fourier-Domain Electromagnetic Wave Theory for Layered Metamaterials of Finite Extent
The Floquet-Bloch theorem allows waves in infinite, lossless periodic media
to be expressed as a sum of discrete Floquet-Bloch modes, but its validity is
challenged under the realistic constraints of loss and finite extent. In this
work, we mathematically reveal the existence of Floquet-Bloch modes in the
electromagnetic fields sustained by lossy, finite periodic layered media using
Maxwell's equations alone without invoking the Floquet-Bloch theorem. Starting
with a transfer-matrix representation of the electromagnetic field in a generic
layered medium, we apply Fourier transformation and a series of mathematical
manipulations to isolate a term explicitly dependent on Floquet-Bloch modes.
Fourier-domain representation of the electromagnetic field can be reduced into
a product of the Floquet-Bloch term and two other matrix factors: one governed
by reflections from the medium boundaries and another dependent on layer
composition. Electromagnetic fields in any finite, lossy, layered structure can
now be interpreted in the Fourier-domain by separable factors dependent on
distinct physical features of the structure. The developed theory enables new
methods for analyzing and communicating the electromagnetic properties of
layered metamaterials.Comment: 10 pages, 3 figure
Demonstration of amplitude-distortion correction by modal dispersal and phase conjugation
We demonstrate experimentally and explain theoretically polarization-preserving imaging through a lossy amplitude-distorting medium. This is accomplished by propagating the beam, before its arrival at the lossy distorting medium, through a (multi) mode- and polarization-scrambling fiber and reflecting the signal, after it has passed the lossy distorting medium, from a photorefractive phase-conjugate mirror
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