Source Resolvability and Intrinsic Randomness: Two Random Number Generation Problems with Respect to a Subclass of f-Divergences

Ryo Nomura*

*この研究の対応する著者

研究成果査読

2 被引用数 (Scopus)

抄録

This paper deals with two typical random number generation problems in information theory. One is the source resolvability problem (resolvability problem for short) and the other is the intrinsic randomness problem. In the literature, optimum achievable rates in these two problems 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 these two problems with respect to f-divergences. The f-divergence is a general non-negative measure between two probabilistic distributions on the basis of a convex function f. The class of f-divergences includes several important measures such as the variational distance, the KL divergence, the Hellinger distance and so on. Hence, it is meaningful to consider the random number generation problems with respect to f-divergences. In this paper, we impose some conditions on the function f so as to simplify the analysis, that is, we consider a subclass of f-divergences. Then, we first derive general formulas of the first-order optimum achievable rates with respect to f-divergences. Next, we particularize our general formulas to several specified functions f. As a result, we reveal that it is easy to derive optimum achievable rates for several important measures from our general formulas. The second-order optimum achievable rates and optimistic optimum achievable rates have also been investigated.

本文言語English
論文番号9140025
ページ(範囲)7588-7601
ページ数14
ジャーナルIEEE Transactions on Information Theory
66
12
DOI
出版ステータスPublished - 2020 12

ASJC Scopus subject areas

  • 情報システム
  • コンピュータ サイエンスの応用
  • 図書館情報学

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