TY - GEN
T1 - Intrinsic Randomness Problem with Respect to a Subclass of f-divergence
AU - Nomura, Ryo
N1 - Funding Information:
ACKNOWLEDGMENT This work was supported in part by JSPS KAKENHI Grant Number JP18K04150.
Publisher Copyright:
© 2019 IEEE.
PY - 2019/8
Y1 - 2019/8
N2 - This paper deals with the intrinsic randomness (IR) problem, which is one of typical random number generation problems. In the literature, the optimum achievable rates in the IR problem with respect to the variational distance as well as the Kullback-Leibler (KL) divergence have already been analyzed. On the other hand, in this study we consider the IR problem with respect to a subclass of f-divergences. The f-divergence is a general non-negative measure between two probabilistic distributions and includes several important measures such as the total variational distance, the χ2-divergence, the KL divergence, and so on. Hence, it is meaningful to consider the IR problem with respect to the f-divergence. In this paper, we assume some conditions on the f-divergence for simplifying the analysis. That is, we focus on a subclass of f-divergences. In this problem setting, we first derive the general formula of the optimum achievable rate. Next, we show that it is easy to derive the optimum achievable rate with respect to the variational distance, the KL divergence, and the Hellinger distance from our general formula.
AB - This paper deals with the intrinsic randomness (IR) problem, which is one of typical random number generation problems. In the literature, the optimum achievable rates in the IR problem with respect to the variational distance as well as the Kullback-Leibler (KL) divergence have already been analyzed. On the other hand, in this study we consider the IR problem with respect to a subclass of f-divergences. The f-divergence is a general non-negative measure between two probabilistic distributions and includes several important measures such as the total variational distance, the χ2-divergence, the KL divergence, and so on. Hence, it is meaningful to consider the IR problem with respect to the f-divergence. In this paper, we assume some conditions on the f-divergence for simplifying the analysis. That is, we focus on a subclass of f-divergences. In this problem setting, we first derive the general formula of the optimum achievable rate. Next, we show that it is easy to derive the optimum achievable rate with respect to the variational distance, the KL divergence, and the Hellinger distance from our general formula.
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U2 - 10.1109/ITW44776.2019.8989245
DO - 10.1109/ITW44776.2019.8989245
M3 - Conference contribution
AN - SCOPUS:85081104287
T3 - 2019 IEEE Information Theory Workshop, ITW 2019
BT - 2019 IEEE Information Theory Workshop, ITW 2019
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2019 IEEE Information Theory Workshop, ITW 2019
Y2 - 25 August 2019 through 28 August 2019
ER -