Summary
The 2018 International Symposium on Information Theory and Its Applications (ISITA2018)
2018
Session Number:We-PM-2-3
Session:
Number:We-PM-2-3.1
Asymptotic Behavior of Typical Sets and the Smallest High Probability Set
Munenori Eto, Masanori Kawakita, Jun’ichi Takeuchi,
pp.749-753
Publication Date:2018/10/18
Online ISSN:2188-5079
DOI:10.34385/proc.55.We-PM-2-3.1
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Summary:
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.