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Entropy 2017, 19(6), 276; doi:10.3390/e19060276

Noise Enhancement for Weighted Sum of Type I and II Error Probabilities with Constraints

College of Communication Engineering, Chongqing University, Chongqing 400044, China
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Received: 12 April 2017 / Revised: 8 June 2017 / Accepted: 12 June 2017 / Published: 14 June 2017
(This article belongs to the Section Information Theory)
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Abstract

In this paper, the noise-enhanced detection problem is investigated for the binary hypothesis-testing. The optimal additive noise is determined according to a criterion proposed by DeGroot and Schervish (2011), which aims to minimize the weighted sum of type I and II error probabilities under constraints on type I and II error probabilities. Based on a generic composite hypothesis-testing formulation, the optimal additive noise is obtained. The sufficient conditions are also deduced to verify whether the usage of the additive noise can or cannot improve the detectability of a given detector. In addition, some additional results are obtained according to the specificity of the binary hypothesis-testing, and an algorithm is developed for finding the corresponding optimal noise. Finally, numerical examples are given to verify the theoretical results and proofs of the main theorems are presented in the Appendix. View Full-Text
Keywords: noise enhancement; hypothesis testing; weighted sum; error probability noise enhancement; hypothesis testing; weighted sum; error probability
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Liu, S.; Yang, T.; Zhang, K. Noise Enhancement for Weighted Sum of Type I and II Error Probabilities with Constraints. Entropy 2017, 19, 276.

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