Causal coding of markov sources with continuous alphabets

Serdar Yüksel, Tamer Basar

Research output: Chapter in Book/Report/Conference proceedingChapter


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
Number of pages18
ISBN (Print)9783540743576
StatePublished - 2008

ASJC Scopus subject areas

  • General Engineering


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