TY - JOUR

T1 - Variable-length intrinsic randomness on two performance criteria based on variational distance

AU - Yoshizawa, Jun

AU - Saito, Shota

AU - Matsushima, Toshiyasu

N1 - Funding Information:
The authors are very grateful to anonymous reviewers for their helpful comments and suggestions. Also, we would like to thank Dr. Hideki Yagi and Dr. Ryo No-mura for helpful discussions. This work was supported in part by JSPS KAKENHI Grant Numbers JP17K00316, JP17K06446, JP18K11585, and JP19K14989.
Publisher Copyright:
Copyright © 2019 The Institute of Electronics, Information and Communication Engineers.

PY - 2019

Y1 - 2019

N2 - This paper investigates the problem of variable-length intrinsic randomness for a general source. For this problem, we can consider two performance criteria based on the variational distance: the maximum and average variational distances. For the problem of variable-length intrinsic randomness with the maximum variational distance, we derive a general formula of the average length of uniform random numbers. Further, we derive the upper and lower bounds of the general formula and the formula for a stationary memoryless source. For the problem of variable-length intrinsic randomness with the average variational distance, we also derive a general formula of the average length of uniform random numbers.

AB - This paper investigates the problem of variable-length intrinsic randomness for a general source. For this problem, we can consider two performance criteria based on the variational distance: the maximum and average variational distances. For the problem of variable-length intrinsic randomness with the maximum variational distance, we derive a general formula of the average length of uniform random numbers. Further, we derive the upper and lower bounds of the general formula and the formula for a stationary memoryless source. For the problem of variable-length intrinsic randomness with the average variational distance, we also derive a general formula of the average length of uniform random numbers.

KW - Average variational distance

KW - General source

KW - Maximum variational distance

KW - Variable-length intrinsic randomness

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U2 - 10.1587/transfun.E102.A.1642

DO - 10.1587/transfun.E102.A.1642

M3 - Article

AN - SCOPUS:85076416659

SN - 0916-8508

VL - E102A

SP - 1642

EP - 1650

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

IS - 12

ER -