Hypothesis Testing with Privacy Constraints Over A Noisy Channel
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We consider a hypothesis testing problem with privacy constraints over a noisy channel and derive fundamental limits of optimal tests under the Neyman-Pearson criterion. The fundamental limit of interest is the privacy-utility tradeoff (PUT) between the exponent of the type-II error probability and the leakage of the information source subject to a constant constraint on the type-I error probability. We provide exact characterization of the asymptotic PUT for any non-vanishing type-I error probability. In particular, we show that tolerating a larger type-I error probability cannot increase the PUT. Such a result is known as strong converse or strong impossibility theorem. To prove the strong converse theorem, we apply the recently proposed strong converse technique by Tyagi and Watanabe (TIT 2020) and further demonstrate the generality of the technique. The strong converse theorems for several problems, such as hypothesis testing against independence over a noisy channel (Sreekumar and Gündüz, TIT 2020) and hypothesis testing with communication and privacy constraints (Gilani et al., Entropy 2020), are established or recovered as special cases of our result.
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