Variable-Length Intrinsic Randomness on Two Performance Criteria Based on Variational Distance

Jun YOSHIZAWA  Shota SAITO  Toshiyasu MATSUSHIMA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E102-A   No.12   pp.1642-1650
Publication Date: 2019/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E102.A.1642
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Shannon Theory
Keyword: 
average variational distance,  general source,  maximum variational distance,  variable-length intrinsic randomness,  

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Summary: 
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.