### Abstract

Cardinality of typical sets and the smallest high probability set for discrete memoryless sources and stationary Markov sources are considered. Usually, its width is fixed in the definition of both sets, but sometimes it is assumed that the width converges to zero as the length of sequence n goes to infinity. In such setting, some condition for the width is necessary to make the cardinality near 2^{nH}, where H denotes the entropy rate of the information source. In this article, we give sufficient conditions for the above propositions. We also show sufficient conditions for that they don't hold for DMS and Markov sources under a certain restriction.

Original language | English |
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Title of host publication | Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 717-721 |

Number of pages | 5 |

ISBN (Electronic) | 9784885523182 |

DOIs | |

Publication status | Published - Mar 8 2019 |

Event | 15th International Symposium on Information Theory and Its Applications, ISITA 2018 - Singapore, Singapore Duration: Oct 28 2018 → Oct 31 2018 |

### Publication series

Name | Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018 |
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### Conference

Conference | 15th International Symposium on Information Theory and Its Applications, ISITA 2018 |
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Country | Singapore |

City | Singapore |

Period | 10/28/18 → 10/31/18 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Science Applications
- Information Systems

### Cite this

*Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018*(pp. 717-721). [8664327] (Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ISITA.2018.8664327

**Asymptotic Behavior of Typical Sets and the Smallest High Probability Set.** / Eto, Munenori; Kawakita, Masanori; Takeuchi, Junnichi.

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

*Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018.*, 8664327, Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018, Institute of Electrical and Electronics Engineers Inc., pp. 717-721, 15th International Symposium on Information Theory and Its Applications, ISITA 2018, Singapore, Singapore, 10/28/18. https://doi.org/10.23919/ISITA.2018.8664327

}

TY - GEN

T1 - Asymptotic Behavior of Typical Sets and the Smallest High Probability Set

AU - Eto, Munenori

AU - Kawakita, Masanori

AU - Takeuchi, Junnichi

PY - 2019/3/8

Y1 - 2019/3/8

N2 - Cardinality of typical sets and the smallest high probability set for discrete memoryless sources and stationary Markov sources are considered. Usually, its width is fixed in the definition of both sets, but sometimes it is assumed that the width converges to zero as the length of sequence n goes to infinity. In such setting, some condition for the width is necessary to make the cardinality near 2nH, where H denotes the entropy rate of the information source. In this article, we give sufficient conditions for the above propositions. We also show sufficient conditions for that they don't hold for DMS and Markov sources under a certain restriction.

AB - Cardinality of typical sets and the smallest high probability set for discrete memoryless sources and stationary Markov sources are considered. Usually, its width is fixed in the definition of both sets, but sometimes it is assumed that the width converges to zero as the length of sequence n goes to infinity. In such setting, some condition for the width is necessary to make the cardinality near 2nH, where H denotes the entropy rate of the information source. In this article, we give sufficient conditions for the above propositions. We also show sufficient conditions for that they don't hold for DMS and Markov sources under a certain restriction.

UR - http://www.scopus.com/inward/record.url?scp=85063891403&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063891403&partnerID=8YFLogxK

U2 - 10.23919/ISITA.2018.8664327

DO - 10.23919/ISITA.2018.8664327

M3 - Conference contribution

T3 - Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018

SP - 717

EP - 721

BT - Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018

PB - Institute of Electrical and Electronics Engineers Inc.

ER -