 
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
