Relating information-theoretic limits to the lyapunov exponent of a dynamical system

Feedback;Feedforward;Posterior Matching;Lyapunov Exponent

Ebeid, Hani-James M. ; Coleman ; Todd P.

关键词: Feedback;    Feedforward;    Posterior Matching;    Lyapunov Exponent;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/16882/Ebeid_Hani-James.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.