State-Dependent Generalizations of Nonanticipatory Epsilon Entropy of Partially Observable Processes

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Journal Title
Journal ISSN
Volume Title
Conference article in proceedings
Date
2023-01-10
Major/Subject
Mcode
Degree programme
Language
en
Pages
8
7415-7422
Series
2022 IEEE 61st Conference on Decision and Control (CDC)
Abstract
Two fundamental generalizations of Gorbunov’s and Pinsker’s nonanticipatory ϵ−entropy are formulated and analyzed for a tuple of partially observable, finite-dimensional, random processes (Xn,Yn), where ${X^n} \triangleq \left\{ {{X_1}, \ldots ,{X_n}} \right\}$ is the unobserved state process and Yn ≜ {Y1,…,Yn} is the observable process-a noisy version of Xn, subject to a fidelity between Xn, and its reproduction ${\hat X^n} \triangleq \left\{ {{{\hat X}_1}, \ldots ,{{\hat X}_n}} \right\}$. The encoder observes causally Yn and past reproductions ${\hat X^n}$ may or may not be available to both the encoder and the decoder. Theorem 1 gives a tight lower bound on the operational rate of zero-delay codes, when ${\hat X^n}$ is causally available to the decoder only, in terms of a state-dependent nonanticipatory ϵ−entropy of a state process Zn, which is fundamentally different from a corresponding nonanticipatory ϵ−entropy, when ${\hat X^n}$ is causally available to both the encoder and the decoder. Theorem 2 identifies sufficient conditions for the two nonanticipatory ϵ−entropies to coincide. Theorem 3 identifies the information structure of the optimal test-channel distributions. The paper also discusses applications to jointly Gaussian partially observable processes (Xn,Yn) with a square-error fidelity criterion, and derives characterizations of the two nonanticipatory ϵ−entropies.
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Keywords
Sufficient conditions, Codes, Process control, Entropy, Decoding, Random processes, Noise measurement
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Citation
Charalambous , C D & Charalambous , T 2023 , State-Dependent Generalizations of Nonanticipatory Epsilon Entropy of Partially Observable Processes . in 2022 IEEE 61st Conference on Decision and Control (CDC) . Proceedings of the IEEE Conference on Decision & Control , IEEE , pp. 7415-7422 , IEEE Conference on Decision and Control , Cancun , Mexico , 06/12/2022 . https://doi.org/10.1109/CDC51059.2022.9992629