### Abstract

This paper considers universal lossless variable-length source coding problem and deals with one of the fundamental limits and pointwise asymptotics of the Bayes code for stationary ergodic finite order Markov sources. As investigation of the fundamental limits, we show upper and lower bounds of the minimum rate such that the probability which exceeds it is less than ϵ ϵ (0, 1). Furthermore, we prove that the codeword length ovf the Bayes code satisfies the asymptotic normality (pointwise equation asymptotics) and the law of the iterated logarithm (pointwise equation asymptotics), where n represents length of a source sequence and 'log' is the natural logarithm.

Original language | English |
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Title of host publication | IEEE International Symposium on Information Theory - Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1986-1990 |

Number of pages | 5 |

Volume | 2015-June |

ISBN (Print) | 9781467377041 |

DOIs | |

Publication status | Published - 2015 Sep 28 |

Event | IEEE International Symposium on Information Theory, ISIT 2015 - Hong Kong, Hong Kong Duration: 2015 Jun 14 → 2015 Jun 19 |

### Other

Other | IEEE International Symposium on Information Theory, ISIT 2015 |
---|---|

Country | Hong Kong |

City | Hong Kong |

Period | 15/6/14 → 15/6/19 |

### Fingerprint

### ASJC Scopus subject areas

- Applied Mathematics
- Modelling and Simulation
- Theoretical Computer Science
- Information Systems

### Cite this

*IEEE International Symposium on Information Theory - Proceedings*(Vol. 2015-June, pp. 1986-1990). [7282803] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2015.7282803

**Fundamental limit and pointwise asymptotics of the Bayes code for Markov sources.** / Saito, Shota; Miya, Nozomi; Matsushima, Toshiyasu.

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

*IEEE International Symposium on Information Theory - Proceedings.*vol. 2015-June, 7282803, Institute of Electrical and Electronics Engineers Inc., pp. 1986-1990, IEEE International Symposium on Information Theory, ISIT 2015, Hong Kong, Hong Kong, 15/6/14. https://doi.org/10.1109/ISIT.2015.7282803

}

TY - GEN

T1 - Fundamental limit and pointwise asymptotics of the Bayes code for Markov sources

AU - Saito, Shota

AU - Miya, Nozomi

AU - Matsushima, Toshiyasu

PY - 2015/9/28

Y1 - 2015/9/28

N2 - This paper considers universal lossless variable-length source coding problem and deals with one of the fundamental limits and pointwise asymptotics of the Bayes code for stationary ergodic finite order Markov sources. As investigation of the fundamental limits, we show upper and lower bounds of the minimum rate such that the probability which exceeds it is less than ϵ ϵ (0, 1). Furthermore, we prove that the codeword length ovf the Bayes code satisfies the asymptotic normality (pointwise equation asymptotics) and the law of the iterated logarithm (pointwise equation asymptotics), where n represents length of a source sequence and 'log' is the natural logarithm.

AB - This paper considers universal lossless variable-length source coding problem and deals with one of the fundamental limits and pointwise asymptotics of the Bayes code for stationary ergodic finite order Markov sources. As investigation of the fundamental limits, we show upper and lower bounds of the minimum rate such that the probability which exceeds it is less than ϵ ϵ (0, 1). Furthermore, we prove that the codeword length ovf the Bayes code satisfies the asymptotic normality (pointwise equation asymptotics) and the law of the iterated logarithm (pointwise equation asymptotics), where n represents length of a source sequence and 'log' is the natural logarithm.

UR - http://www.scopus.com/inward/record.url?scp=84969801339&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84969801339&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2015.7282803

DO - 10.1109/ISIT.2015.7282803

M3 - Conference contribution

AN - SCOPUS:84969801339

SN - 9781467377041

VL - 2015-June

SP - 1986

EP - 1990

BT - IEEE International Symposium on Information Theory - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

ER -