By Topic

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

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

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

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

Published in:

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