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.
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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 -