### Abstract

The objective of this research is to evaluate the ε-minimum overflow threshold of the Bayes codes for a Markov source. In the lossless variable-length source coding problem, typical criteria are the mean codeword length and the overflow probability. The overflow probability is the probability with which a codeword length per source symbol exceeds a threshold and the ε-minimum overflow threshold is defined. In the non-universal setting, the Shannon code is optimal under the mean codeword length and the ε-minimum overflow threshold for the Shannon code is derived for an i.i.d. source. On the other hand, in the universal setting, the Bayes code is one of universal codes which minimize the mean codeword length under the Bayes criterion. However, few studies have been done on the overflow probability for the Bayes codes. In this paper, we assume a stationary ergodic finite order Markov source and derive the upper and lower bounds of the ε-minimum overflow threshold of the Bayes codes.

Original language | English |
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Title of host publication | Proceedings of 2014 International Symposium on Information Theory and Its Applications, ISITA 2014 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 211-215 |

Number of pages | 5 |

ISBN (Electronic) | 9784885522925 |

Publication status | Published - 2014 Dec 8 |

Event | 2014 International Symposium on Information Theory and Its Applications, ISITA 2014 - Melbourne, Australia Duration: 2014 Oct 26 → 2014 Oct 29 |

### Publication series

Name | Proceedings of 2014 International Symposium on Information Theory and Its Applications, ISITA 2014 |
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### Conference

Conference | 2014 International Symposium on Information Theory and Its Applications, ISITA 2014 |
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Country | Australia |

City | Melbourne |

Period | 14/10/26 → 14/10/29 |

### ASJC Scopus subject areas

- Computer Science Applications
- Information Systems

## Cite this

*Proceedings of 2014 International Symposium on Information Theory and Its Applications, ISITA 2014*(pp. 211-215). [6979834] (Proceedings of 2014 International Symposium on Information Theory and Its Applications, ISITA 2014). Institute of Electrical and Electronics Engineers Inc..