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Variable-Length Intrinsic Randomness on Two Performance Criteria Based on Variational Distance
Jun YOSHIZAWA Shota SAITO Toshiyasu MATSUSHIMA
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2019/12/01
Online ISSN: 1745-1337
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Shannon Theory
average variational distance, general source, maximum variational distance, variable-length intrinsic randomness,
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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.