TY - GEN

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

AU - Eto, Munenori

AU - Kawakita, Masanori

AU - Takeuchi, Junrichi

N1 - Funding Information:
ACKNOWLEDGMENT This research was partially supported by JSPS KAKENHI Grant Number 18H03291.

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

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U2 - 10.23919/ISITA.2018.8664327

DO - 10.23919/ISITA.2018.8664327

M3 - Conference contribution

AN - SCOPUS:85063891403

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.

T2 - 15th International Symposium on Information Theory and Its Applications, ISITA 2018

Y2 - 28 October 2018 through 31 October 2018

ER -