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Csisz ar's Cuto Rates for Arbitrary Discrete Sources Po-Ning Chen y and Fady Alajaji z
 

Summary: Csiszar's Cuto Rates for Arbitrary Discrete Sources 
Po-Ning Chen y and Fady Alajaji z
y Department of Communication Engineering
National Chiao-Tung 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 de ned
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 xed-length source coding operational

  

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

 

Collections: Engineering