Zero-Delay Lossy Coding of Linear Vector Markov Sources with Applications to Networked Control
Loading...
Authors
Ghomi, Meysam
Date
Type
thesis
Language
eng
Keyword
Zero-Delay Coding , Stochastic Control , Information Theorey , Markov Decision Process , Stochastic Control
Alternative Title
Abstract
In this thesis we study the optimal zero-delay coding (quantization) of $\mathbb{R}^d$-valued linearly
generated Markov sources under quadratic distortion. The structure and existence of
deterministic and stationary coding policies that are optimal for the infinite horizon average
cost (distortion) problem is established. Prior results studying the optimality
of zero-delay codes for Markov sources for infinite horizons either considered finite
alphabet sources or, for the $\mathbb{R}^d$-valued case, only showed the
existence of deterministic and non-stationary Markov coding policies or those
which are randomized. In addition to existence results, for finite blocklength
(horizon) $T$ the performance of an optimal coding policy is shown to approach
the infinite time horizon optimum at a rate $O(\frac{1}{T})$. This gives an
explicit rate of convergence that quantifies the near-optimality of finite window (finite-memory)
codes among all optimal zero-delay codes. In addition, we present an important application of our result to closed loop networked control systems. We show that with predictive encoder the separation principle for the infinite horizon problem holds. Prior results only proved this for finite horizon average cost problem.
Description
Citation
Publisher
License
Queen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canada
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
CC0 1.0 Universal
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
CC0 1.0 Universal