TY - GEN

T1 - Intrinsic Randomness Problem with Respect to a Subclass of f-divergence

AU - Nomura, Ryo

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.

UR - http://www.scopus.com/inward/record.url?scp=85081104287&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85081104287&partnerID=8YFLogxK

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 -