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- W2971322685 abstract "We consider the problem of optimal zero-delay coding and estimation of a stochastic dynamical system over a noisy communication channel under three estimation criteria concerned with the low-distortion regime. The criteria considered are (i) a strong and (ii) a weak form of almost sure stability of the estimation error as well as (ii) asymptotic quadratic stability in expectation. For all three objectives, we derive lower bounds on the smallest channel capacity C <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>0</sub> above which the objective can be achieved with an arbitrarily small error. We first obtain bounds through a dynamical systems approach by constructing an infinite-dimensional dynamical system and relating the capacity with the topological and the metric entropy of this system. We also consider information-theoretic and probability-theoretic approaches to address the different criteria. Finally, we prove that a memoryless noisy channel in general constitutes no obstruction to asymptotic almost sure state estimation with arbitrarily small errors, when there is no noise in the system. The results provide new solution methods for the criteria introduced (e.g., standard information-theoretic bounds cannot be applied for some of the criteria) and establish further connections between dynamical systems, networked control, and information theory, especially in the context of nonlinear stochastic systems." @default.
- W2971322685 created "2019-09-05" @default.
- W2971322685 creator A5005401257 @default.
- W2971322685 creator A5059120486 @default.
- W2971322685 date "2020-06-01" @default.
- W2971322685 modified "2023-10-02" @default.
- W2971322685 title "Metric and Topological Entropy Bounds for Optimal Coding of Stochastic Dynamical Systems" @default.
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- W2971322685 doi "https://doi.org/10.1109/tac.2019.2937732" @default.
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