Relating information-theoretic limits to the lyapunov exponent of a dynamical system
Ebeid, Hani-James M.
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https://hdl.handle.net/2142/16882
Description
Title
Relating information-theoretic limits to the lyapunov exponent of a dynamical system
Author(s)
Ebeid, Hani-James M.
Issue Date
2010-08-20T18:00:41Z
Director of Research (if dissertation) or Advisor (if thesis)
Coleman, Todd P.
Department of Study
Electrical & Computer Eng
Discipline
Electrical & Computer Engr
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Date of Ingest
2010-08-20T18:00:41Z
Keyword(s)
Feedback
Feedforward
Posterior Matching
Lyapunov Exponent
Abstract
In this thesis we use control theoretic techniques to provide a new perspective for analyzing some problems in information theory. In particular, we explore two related data dissemination problems - channel coding with feedback and source coding with feedforward - and see that the Lyapunov exponent of a related dynamical system emerges as a fundamental quantity. For channel coding with feedback, we show that for a broad class of channels - both with and without memory - the Lyapunov exponent of the transmission function is fundamentally linked to the maximum rate which the scheme can attain. We note that the posterior matching scheme - a provably optimal feedback communication scheme for memoryless channels - has an encoding function with a Lyapunov exponent exactly equal to the communication rate. In the dual problem, source coding with feedforward, the optimal test channel is memoryless. This motivates the idea of dualizing posterior matching for this setting. By exploiting the Lyapunov exponent property, we demonstrate that such a scheme - with low decoder complexity - attains the rate-distortion function. By approaching these problems from a dynamical systems perspective, we hope to provide the intuition to motivate the evaluation and design of new communication schemes.
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