Causal coding of markov sources with continuous alphabets

Serdar Yüksel, Tamer Basar

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We study, for kth-order Markov sources, the structure of optimal causal encoders minimizing total rate subject to a mean-square distortion constraint over a finite horizon. The class of sources considered is general alphabet sources, and the encoder is allowed to be variable-rate. This leads to an optimization problem in an infinite-dimensional space, for which a solution exists. We show that the optimal causal encoder for a kth-order Markov source uses only the most recent k source symbols and the information available at the receiver. We also consider the infinite-horizon version, but for k=1, provide an existence result for an optimal stationary solution, discuss the effect of randomization on performance, and show that a recurrence-based time sharing of at most two deterministic quantizers is optimal. We further argue that for real-valued processes innovation encoding is not in general optimal, but for coding of a stable linear or non-linear source, the quantization of the innovation is an almost optimal scheme in the limit of low-distortion. This class of problems has natural applications in remote control of linear and non-linear systems with quantization.

Original languageEnglish (US)
Title of host publicationAnalysis and Design of Nonlinear Control Systems
Subtitle of host publicationIn Honor of Alberto Isidori
PublisherSpringer Berlin Heidelberg
Pages91-108
Number of pages18
ISBN (Print)9783540743576
DOIs
StatePublished - Dec 1 2008

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Innovation
Remote control
Nonlinear systems

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Yüksel, S., & Basar, T. (2008). Causal coding of markov sources with continuous alphabets. In Analysis and Design of Nonlinear Control Systems: In Honor of Alberto Isidori (pp. 91-108). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-74358-3_7

Causal coding of markov sources with continuous alphabets. / Yüksel, Serdar; Basar, Tamer.

Analysis and Design of Nonlinear Control Systems: In Honor of Alberto Isidori. Springer Berlin Heidelberg, 2008. p. 91-108.

Research output: Chapter in Book/Report/Conference proceedingChapter

Yüksel, S & Basar, T 2008, Causal coding of markov sources with continuous alphabets. in Analysis and Design of Nonlinear Control Systems: In Honor of Alberto Isidori. Springer Berlin Heidelberg, pp. 91-108. https://doi.org/10.1007/978-3-540-74358-3_7
Yüksel S, Basar T. Causal coding of markov sources with continuous alphabets. In Analysis and Design of Nonlinear Control Systems: In Honor of Alberto Isidori. Springer Berlin Heidelberg. 2008. p. 91-108 https://doi.org/10.1007/978-3-540-74358-3_7
Yüksel, Serdar ; Basar, Tamer. / Causal coding of markov sources with continuous alphabets. Analysis and Design of Nonlinear Control Systems: In Honor of Alberto Isidori. Springer Berlin Heidelberg, 2008. pp. 91-108
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