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

Ryo Nomura*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number9140025
Pages (from-to)7588-7601
Number of pages14
JournalIEEE Transactions on Information Theory
Volume66
Issue number12
DOIs
Publication statusPublished - 2020 Dec

Keywords

  • Kullback-Leibler divergence
  • f-divergence
  • general source
  • information-spectrum methods
  • intrinsic randomness
  • source resolvability
  • variational distance

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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