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One-shot achievability via fidelity

Yassaee, M. H ; Sharif University of Technology | 2015

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  1. Type of Document: Article
  2. DOI: 10.1109/ISIT.2015.7282465
  3. Publisher: 2015
  4. Abstract:
  5. This paper provides a universal framework for establishing one-shot achievability results for coordination and secrecy problems. The framework is built on our previous framework [Yassaee et al. 13] for proving one-shot achievability results in the context of source and channel coding problems. In the coordination and secrecy problems, one needs to compare an induced distribution by encoding/decoding with an ideal distribution (satisfying some desirable properties) using a suitable criterion. In this paper, we use fidelity as a criterion for measuring the closeness of induced distribution with the ideal distribution. The framework exploits the stochastic mutual information coders at the encoders and decoders and uses Jensen's inequality to find a lower bound on the expected fidelity. Moreover, the framework employs Cauchy-Schwarz inequality to simplify the relations prior to applying Jensen's inequality. We illustrate the framework via channel synthesis problem and wiretap channel. Furthermore, a novel one-shot generalization of multivariate covering lemma and soft covering lemma (cf. Cuff'13) is established
  6. Keywords:
  7. Stochastic systems ; Cauchy-Schwarz inequality ; Encoders and decoders ; Encoding/decoding ; Jensen's inequality ; Mutual informations ; Source and channel coding ; Synthesis problems ; Wire-tap channels ; Information theory
  8. Source: IEEE International Symposium on Information Theory - Proceedings, 14 June 2015 through 19 June 2015 ; Volume 2015-June , 2015 , Pages 301-305 ; 21578095 (ISSN) ; 9781467377041 (ISBN)
  9. URL: http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=7282465&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D7282465