### 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 (Print) | 9784885522925 |

Publication status | Published - 2014 Dec 8 |

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

### Other

Other | 2014 International Symposium on Information Theory and Its Applications, ISITA 2014 |
---|---|

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] Institute of Electrical and Electronics Engineers Inc..

**Evaluation of the minimum overflow threshold of bayes codes for a Markov source.** / Saito, Shota; Miya, Nozomi; Matsushima, Toshiyasu.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of 2014 International Symposium on Information Theory and Its Applications, ISITA 2014.*, 6979834, Institute of Electrical and Electronics Engineers Inc., pp. 211-215, 2014 International Symposium on Information Theory and Its Applications, ISITA 2014, Melbourne, 14/10/26.

}

TY - GEN

T1 - Evaluation of the minimum overflow threshold of bayes codes for a Markov source

AU - Saito, Shota

AU - Miya, Nozomi

AU - Matsushima, Toshiyasu

PY - 2014/12/8

Y1 - 2014/12/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84920516110&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84920516110&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9784885522925

SP - 211

EP - 215

BT - Proceedings of 2014 International Symposium on Information Theory and Its Applications, ISITA 2014

PB - Institute of Electrical and Electronics Engineers Inc.

ER -