One-shot achievability via fidelity

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.