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Csiszar's cutoff rates for arbitrary discrete sources

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2 Author(s)
Po-Ning Chen ; Dept. of Commun. Eng., Nat. Chiao Tung Univ., Hsinchu, Taiwan ; Alajaji, F.

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

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Information Theory, IEEE Transactions on  (Volume:47 ,  Issue: 1 )