Csiszar's cutoff rates for arbitrary discrete sources

Abstract

Csiszar's forward beta -cutoff rate (given a fixed beta > 0) for a discrete source is defined as the smallest number Ro such that for every R > R-0, there exists a sequence of tired-length codes of rate R with probability of error asymptotically vanishing as e(-n beta (R-R0)). For a discrete memoryless source (DMS), the forward beta -cutoff rate is shown by Csiszar [6] to be equal to the source Renyi entropy. An analogous concept of reverse beta -cutoff 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 beta -cutoff 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 beta -cutoff rates, respectively. Consequently, new fixed-length source coding operational characterizations for the Renyi entropy rates are established.