Csiszar's cutoff rates for arbitrary discrete sources

Csiszar's (1995) forward /spl beta/-cutoff rate (given a fixed /spl beta/>0) for a discrete source is defined as the smallest number R/sub 0/ such that for every R>R/sub 0/, there exists a sequence of fixed-length codes of rate R with probability of error asymptotically vanishing as e/sup -n/spl beta/(R-R0)/. For a discrete memoryless source (DMS), the forward /spl beta/-cutoff rate is shown by Csiszar to be equal to the source Renyi (1961) entropy. An analogous concept of reverse /spl 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 /spl 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 /spl beta/-cutoff rates, respectively. Consequently, new fixed-length source coding operational characterizations for the Renyi entropy rates are established.