## Abstract

Csiszár's forward β-cutoff rate (given a fixed β > O) for a discrete source is defined as the smallest number R _{0} such that for every R > R _{0}, 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 Csiszár [6] to be equal to the source Rényi entropy. An analogous concept of reverse β-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 β-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 β-cutoff rates, respectively. Consequently, new fixed-length source coding operational characterizations for the Rényi entropy rates are established.

Original language | English |
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Article number | 904531 |

Pages (from-to) | 330-338 |

Number of pages | 9 |

Journal | IEEE Transactions on Information Theory |

Volume | 47 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2001 |

## Keywords

- Arbitrary sources with memory
- Cutoff rates
- Fixed-length source coding
- Probability of error
- Renji's entropy rates
- Source reliability function