Csiszar´s cutoff rates for arbitrary discrete sources

Csiszar´s (1995) forward β-cutoff rate (given a fixed β>0) for a discrete source is defined as the smallest number R ₀ such that for every R>R₀, 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 Csiszar to be equal to the source Renyi (1961) entropy. An analogous concept of reverse β-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 β-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 β-cutoff rates, respectively. Consequently, new fixed-length source coding operational characterizations for the Renyi entropy rates are established