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Optimal bi-level quantization of i.i.d. sensor observations for binary hypothesis testing

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3 Author(s)
Qian Zhang ; Analog Devices Inc., Norwood, MA, USA ; Varshney, P.K. ; Wesel, R.D.

We consider the problem of binary hypothesis testing using binary decisions from independent and identically distributed (i.i.d). sensors. Identical likelihood-ratio quantizers with threshold λ are used at the sensors to obtain sensor decisions. Under this condition, the optimal fusion rule is known to be a k-out-of-n rule with threshold k. For the Bayesian detection problem, we show that given k, the probability of error is a quasi-convex function of λ and has a single minimum that is achieved by the unique optimal λopt . Except for the trivial situation where one hypothesis is always decided, we obtain a sufficient and necessary condition on λopt, and show that λopt can be efficiently obtained via the SECANT algorithm. The overall optimal solution is obtained by optimizing every pair of (k, λ). For the Neyman-Pearson detection problem, we show that the use of the Lagrange multiplier method is justified for a given fixed k since the objective function is a quasi-convex function of λ. We further show that the receiver operating characteristic (ROC) for a fixed k is concave downward

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Information Theory, IEEE Transactions on  (Volume:48 ,  Issue: 7 )