TY - JOUR

T1 - Csiszar's cutoff rates for arbitrary discrete sources

AU - Chen, Po-Ning

AU - Alajaji, Fady

PY - 2001/1/1

Y1 - 2001/1/1

N2 - Csiszár's forward β-cutoff rate (given a fixed β > O) for a discrete source is defined as the smallest number R 0 such that for every R > R 0, there exists a sequence of fixed-length codes of rate R with probability of error asymptotically vanishing as e -nβ(R-R0). For a discrete memoryless source (DMS), the forward β-cutoff rate is shown by Csiszár [6] to be equal to the source Rényi entropy. An analogous concept of reverse β-cutoff rate regarding the probability of correct decoding is also characterized by Csiszár in terms of the Rényi entropy. In this work, Csiszár's results are generalized by investigating the β-cutoff rates for the class of arbitrary discrete sources with memory. It is demonstrated that the limsup and liminf Rényi entropy rates provide the formulas for the forward and reverse β-cutoff rates, respectively. Consequently, new fixed-length source coding operational characterizations for the Rényi entropy rates are established.

AB - Csiszár's forward β-cutoff rate (given a fixed β > O) for a discrete source is defined as the smallest number R 0 such that for every R > R 0, there exists a sequence of fixed-length codes of rate R with probability of error asymptotically vanishing as e -nβ(R-R0). For a discrete memoryless source (DMS), the forward β-cutoff rate is shown by Csiszár [6] to be equal to the source Rényi entropy. An analogous concept of reverse β-cutoff rate regarding the probability of correct decoding is also characterized by Csiszár in terms of the Rényi entropy. In this work, Csiszár's results are generalized by investigating the β-cutoff rates for the class of arbitrary discrete sources with memory. It is demonstrated that the limsup and liminf Rényi entropy rates provide the formulas for the forward and reverse β-cutoff rates, respectively. Consequently, new fixed-length source coding operational characterizations for the Rényi entropy rates are established.

KW - Arbitrary sources with memory

KW - Cutoff rates

KW - Fixed-length source coding

KW - Probability of error

KW - Renji's entropy rates

KW - Source reliability function

UR - http://www.scopus.com/inward/record.url?scp=0035091412&partnerID=8YFLogxK

U2 - 10.1109/18.904531

DO - 10.1109/18.904531

M3 - Article

AN - SCOPUS:0035091412

SN - 0018-9448

VL - 47

SP - 330

EP - 338

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 1

M1 - 904531

ER -