Shannon Entropy And Tracking Dynamic Systems Over Noisy Channels

Document Type: Article

Author

Department of Electrical Engineering at Sharif University of Technology

Abstract

This paper is concerned with the estimation of state trajectory of linear discrete time
dynamic systems subject to parametric uncertainty over the compound erasure channel
that uses feedback channel intermittently. For this combined system and channel,
using the data processing inequality and a robust version of the Shannon lower bound,
a necessary condition on channel capacity for estimation of state trajectory at the
receiver giving almost sure asymptotically zero estimation error is presented. Then,
an estimation technique over the compound erasure channel that includes an encoder,
decoder and a sucient condition under which the estimation error at the receiver
is asymptotically zero almost surely is presented. This leads to the conclusion that
over the compound erasure channel, a condition on Shannon capacity in terms of
the rate of expansion of the Shannon entropy is a necessary and sucient condition
for estimation with uniform almost sure asymptotically zero estimation error. The
satisfactory performance of the proposed technique is illustrated using simulation.

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Volume 25, Issue 6
Transactions on Computer Science & Engineering and Electrical Engineering (D)
November and December 2018
Pages 3517-3531