TY - GEN

T1 - Variable-Length Intrinsic Randomness Allowing Positive Value of the Average Variational Distance

AU - Yoshizawa, Jun

AU - Saito, Shota

AU - Matsushima, Toshiyasu

N1 - Funding Information:
ACKNOWLEDGMENT The authors would like to thank Dr. Hideki Yagi and Dr. Ryo Nomura for helpful discussions. This work was supported in part by JSPS KAKENHI Grant Numbers JP16K00195, JP16K00417, JP17K00316, JP17K06446.

PY - 2019/3/8

Y1 - 2019/3/8

N2 - This paper considers the problem of variable-length intrinsic randomness. We propose the average variational distance as the performance criterion from the viewpoint of a dual relationship with the problem formulation of variable-length resolvability. Previous study has derived the general formula of the ϵ-variable-length resolvability. We derive the general formula of the ϵ-variable-length intrinsic randomness. Namely, we characterize the supremum of the mean length under the constraint that the value of the average variational distance is smaller than or equal to a constant ϵ. Our result clarifies a dual relationship between the general formula of ϵ-variable-length resolvability and that of ϵ-variable-length intrinsic randomness. We also derive a lower bound of the quantity characterizing our general formula.

AB - This paper considers the problem of variable-length intrinsic randomness. We propose the average variational distance as the performance criterion from the viewpoint of a dual relationship with the problem formulation of variable-length resolvability. Previous study has derived the general formula of the ϵ-variable-length resolvability. We derive the general formula of the ϵ-variable-length intrinsic randomness. Namely, we characterize the supremum of the mean length under the constraint that the value of the average variational distance is smaller than or equal to a constant ϵ. Our result clarifies a dual relationship between the general formula of ϵ-variable-length resolvability and that of ϵ-variable-length intrinsic randomness. We also derive a lower bound of the quantity characterizing our general formula.

UR - http://www.scopus.com/inward/record.url?scp=85063914269&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063914269&partnerID=8YFLogxK

U2 - 10.23919/ISITA.2018.8664364

DO - 10.23919/ISITA.2018.8664364

M3 - Conference contribution

AN - SCOPUS:85063914269

T3 - Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018

SP - 354

EP - 358

BT - Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 15th International Symposium on Information Theory and Its Applications, ISITA 2018

Y2 - 28 October 2018 through 31 October 2018

ER -