Summary: R '
ENYI'S ENTROPY RATE FOR DISCRETE MARKOV SOURCES
Ziad Rached, Fady Alajaji and L. L. Campbell
Dept. of Mathematics and Statistics
Queen's University
Kingston, ON K7L 3N6, Canada
Email: rachedz@shannon.mast.queensu.ca
ABSTRACT
In this work, we extend a variable­length source cod­
ing theorem for discrete memoryless sources to ergodic
time­invariant Markov sources of arbitrary order. To ac­
complish this extension, we establish a formula for the
R'enyi entropy rate limn!1 H ff (n)=n. The main tool used
to obtain the R'enyi entropy rate result is Perron­Frobenius
theory. We also examine the expression of the R'enyi en­
tropy rate for specific examples of Markov sources and in­
vestigate its limit as ff ! 1 and as ff ! 0. Finally, we
conclude with numerical examples.
1. INTRODUCTION
Consider a discrete source fXng; n = 1; 2; : : : with alphabet

Source: Alajaji, Fady - Department of Mathematics and Statistics, Queen's University (Kingston)

Collections: Engineering