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

13 years 4 months ago

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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 are used at the sensors to obtain sensor decisions. Under this condition, the optimal fusion rule is known to be a -out-of- rule with threshold . For the Bayesian detection problem, we show that given , the probability of error is a quasiconvex function of and has a single minimum that is achieved by the unique optimal . Except for the trivial situation where one hypothesis is always decided, we obtain a sufficient and necessary condition on , and show that can be efficiently obtained via the SECANT algorithm. The overall optimal solution is obtained by optimizing every pair of ( ). For the Neyman

Qian Zhang, Pramod K. Varshney, Richard D. Wesel

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