Optimum Intrinsic Randomness Rate with Respect to f -Divergences Using the Smooth Min Entropy

Ryo Nomura; Hideki Yagi

doi:10.1109/ISIT45174.2021.9517784

Optimum Intrinsic Randomness Rate with Respect to f -Divergences Using the Smooth Min Entropy

Ryo Nomura, Hideki Yagi

Center for Data Science

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

1 Citation (Scopus)

Abstract

The intrinsic randomness (IR) problem is considered for general setting. In the literature, the optimum IR rate with respect to the variational distance has been characterized in two ways. One is based on the information spectrum quantity and the other is based on the smooth Rényi entropy. Recently, Nomura has revealed the optimum IR rate with respect to f-divergences, which includes the variational distance, the Kullback-Leibler (KL) divergence and so on, by using the informational spectrum quantity. In this paper, we try to characterize the optimum IR rate with respect to a subclass of f-divergences by using the smooth Min entropy. The subclass of f-divergences considered in this paper includes typical distance measures such as the total variational distance, the KL divergence, the Hellinger distance and so on.

Original language	English
Title of host publication	2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1784-1789
Number of pages	6
ISBN (Electronic)	9781538682098
DOIs	https://doi.org/10.1109/ISIT45174.2021.9517784
Publication status	Published - 2021 Jul 12
Event	2021 IEEE International Symposium on Information Theory, ISIT 2021 - Virtual, Melbourne, Australia Duration: 2021 Jul 12 → 2021 Jul 20

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2021-July
ISSN (Print)	2157-8095

Conference

Conference	2021 IEEE International Symposium on Information Theory, ISIT 2021
Country/Territory	Australia
City	Virtual, Melbourne
Period	21/7/12 → 21/7/20

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Modelling and Simulation
Applied Mathematics

Access to Document

10.1109/ISIT45174.2021.9517784

Cite this

Nomura, R., & Yagi, H. (2021). Optimum Intrinsic Randomness Rate with Respect to f -Divergences Using the Smooth Min Entropy. In 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings (pp. 1784-1789). (IEEE International Symposium on Information Theory - Proceedings; Vol. 2021-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT45174.2021.9517784

Optimum Intrinsic Randomness Rate with Respect to f -Divergences Using the Smooth Min Entropy. / Nomura, Ryo; Yagi, Hideki.
2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2021. p. 1784-1789 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2021-July).

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

Nomura, R & Yagi, H 2021, Optimum Intrinsic Randomness Rate with Respect to f -Divergences Using the Smooth Min Entropy. in 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings. IEEE International Symposium on Information Theory - Proceedings, vol. 2021-July, Institute of Electrical and Electronics Engineers Inc., pp. 1784-1789, 2021 IEEE International Symposium on Information Theory, ISIT 2021, Virtual, Melbourne, Australia, 21/7/12. https://doi.org/10.1109/ISIT45174.2021.9517784

Nomura R, Yagi H. Optimum Intrinsic Randomness Rate with Respect to f -Divergences Using the Smooth Min Entropy. In 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2021. p. 1784-1789. (IEEE International Symposium on Information Theory - Proceedings). doi: 10.1109/ISIT45174.2021.9517784

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abstract = "The intrinsic randomness (IR) problem is considered for general setting. In the literature, the optimum IR rate with respect to the variational distance has been characterized in two ways. One is based on the information spectrum quantity and the other is based on the smooth R{\'e}nyi entropy. Recently, Nomura has revealed the optimum IR rate with respect to f-divergences, which includes the variational distance, the Kullback-Leibler (KL) divergence and so on, by using the informational spectrum quantity. In this paper, we try to characterize the optimum IR rate with respect to a subclass of f-divergences by using the smooth Min entropy. The subclass of f-divergences considered in this paper includes typical distance measures such as the total variational distance, the KL divergence, the Hellinger distance and so on. ",

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Optimum Intrinsic Randomness Rate with Respect to f -Divergences Using the Smooth Min Entropy

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