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Weyl-Heisenberg representation in classical and quantum communications
Applied Math| Speaker: | Peter Jung, Heinrich-Hertz Institute, Berlin |
| Location: | 2112 MSB |
| Start time: | Fri, Jan 26 2007, 3:10PM |
Description
Weyl-Heisenberg type representations occur in several areas of
communication theory. This talk considers examples from
signal theory in doubly dispersive channels and the transmission of
classical information through (bosonic) i.i.d. quantum Gaussian channel.
Both of them can be formulated in a joint framework with similar
performance characterizations based on quantities
called channel fidelities. The first case covers the problem
of the approximate eigenstructure of time-varying channels which is
important for an information-theoretic treatment of communication.
Furthermore, pulse shaping with respect to the scattering function of
wide sense stationary
uncorrelated scattering (WSSUS) mobile communication channels is discussed.
Interestingly, this topic is intimately connected to the problem of quantum
state design for optimal hypothesis testing in Gaussian channels.
A formulation based on the notion of Weyl--Heisenberg maps is presented and
further investigated in terms of scaling behavior and upper bounds.