TY - GEN

T1 - Optimum Source Resolvability Rate with Respect to f-Divergences Using the Smooth Rényi Entropy

AU - Nomura, Ryo

AU - Yagi, Hideki

N1 - Funding Information:
This work was supported in part by JSPS KAKENHI Grant Number, JP16K06340, JP18H01438, JP17K00020, and JP18K04150.

PY - 2020/6

Y1 - 2020/6

N2 - The source resolvability problem (or resolvability problem for short) is one of random number generation problems in information theory. In the literature, the optimum achievable rates in the resolvability problem have been characterized in different 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 achievable rate with respect to the f-divergence, which includes the variational distance, the Kullback-Leibler (KL) divergence and so on. On the other hand, the optimum achievable rates with respect to the variational distance has been characterized by using the smooth Rényi entropy. In this paper, we try to extend this result to the case of other distances. To do so, we consider the resolvability problem with respect to the subclass of f-divergences and determine the optimum achievable rate in terms of the smooth Rényi 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.

AB - The source resolvability problem (or resolvability problem for short) is one of random number generation problems in information theory. In the literature, the optimum achievable rates in the resolvability problem have been characterized in different 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 achievable rate with respect to the f-divergence, which includes the variational distance, the Kullback-Leibler (KL) divergence and so on. On the other hand, the optimum achievable rates with respect to the variational distance has been characterized by using the smooth Rényi entropy. In this paper, we try to extend this result to the case of other distances. To do so, we consider the resolvability problem with respect to the subclass of f-divergences and determine the optimum achievable rate in terms of the smooth Rényi 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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U2 - 10.1109/ISIT44484.2020.9174531

DO - 10.1109/ISIT44484.2020.9174531

M3 - Conference contribution

AN - SCOPUS:85090406062

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2286

EP - 2291

BT - 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2020 IEEE International Symposium on Information Theory, ISIT 2020

Y2 - 21 July 2020 through 26 July 2020

ER -