 
Summary: Csiszar's Cuto Rates for Arbitrary Discrete Sources
PoNing Chen y and Fady Alajaji z
y Department of Communication Engineering
National ChiaoTung University
HsinChu, Taiwan, R.O.C.
z Department of Mathematics and Statistics
Queen's University
Kingston, Ontario K7L 3N6, Canada
Abstract
Csiszar's forward cuto rate (given a xed > 0) for a discrete source is dened
as the smallest number R 0 such that for every R > R 0 , there exists a sequence of xed
length codes of rate R with probability of error asymptotically vanishing as e n(R R 0 ) .
For a discrete memoryless source, the forward cuto rate is shown by Csiszar [6] to
be equal to the source Renyi entropy. An analogous concept of reverse cuto rate
regarding the probability of correct decoding is also characterized by Csiszar in terms
of the Renyi entropy.
In this work, Csiszar's results are generalized by investigating the cuto rates
for the class of arbitrary discrete sources with memory. It is demonstrated that the
limsup and liminf Renyi entropy rates provide the formulas for the forward and reverse
cuto rates, respectively. Consequently, new xedlength source coding operational
