11,766 research outputs found
Partial decode-forward for quantum relay channels
A relay channel is one in which a Source and Destination use an intermediate
Relay station in order to improve communication rates. We propose the study of
relay channels with classical inputs and quantum outputs and prove that a
"partial decode and forward" strategy is achievable. We divide the channel uses
into many blocks and build codes in a randomized, block-Markov manner within
each block. The Relay performs a standard Holevo-Schumacher-Westmoreland
quantum measurement on each block in order to decode part of the Source's
message and then forwards this partial message in the next block. The
Destination performs a novel "sliding-window" quantum measurement on two
adjacent blocks in order to decode the Source's message. This strategy achieves
non-trivial rates for classical communication over a quantum relay channel.Comment: 7 pages, submission to the 2012 International Symposium on
Information Theory (ISIT 2012), Boston, MA, US
The scattering map in two coupled piecewise-smooth systems, with numerical application to rocking blocks
We consider a non-autonomous dynamical system formed by coupling two
piecewise-smooth systems in \RR^2 through a non-autonomous periodic
perturbation. We study the dynamics around one of the heteroclinic orbits of
one of the piecewise-smooth systems. In the unperturbed case, the system
possesses two normally hyperbolic invariant manifolds of dimension two
with a couple of three dimensional heteroclinic manifolds between them. These
heteroclinic manifolds are foliated by heteroclinic connections between
tori located at the same energy levels. By means of the {\em impact map} we
prove the persistence of these objects under perturbation. In addition, we
provide sufficient conditions of the existence of transversal heteroclinic
intersections through the existence of simple zeros of Melnikov-like functions.
The heteroclinic manifolds allow us to define the {\em scattering map}, which
links asymptotic dynamics in the invariant manifolds through heteroclinic
connections. First order properties of this map provide sufficient conditions
for the asymptotic dynamics to be located in different energy levels in the
perturbed invariant manifolds. Hence we have an essential tool for the
construction of a heteroclinic skeleton which, when followed, can lead to the
existence of Arnol'd diffusion: trajectories that, on large time scales,
destabilize the system by further accumulating energy. We validate all the
theoretical results with detailed numerical computations of a mechanical system
with impacts, formed by the linkage of two rocking blocks with a spring
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