Csiszár's cutoff rates for arbitrary discrete sources

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