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Extremal properties of likelihood-ratio quantizers

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1 Author(s)
Tsitsiklis, J.N. ; Lab. for Inf. & Decision Syst., MIT, Cambridge, MA, USA

M hypotheses and a random variable Y with a different probability distribution under each hypothesis are considered. A quantizer is applied to form a quantized random variable γ(Y ). The extreme points of the set of possible probability distributions of γ(Y), as γ ranges over all quantizers, is characterized. Optimality properties of likelihood-ratio quantizers are established for a very broad class of quantization problems, including problems involving the maximization of an Ali-Silvey (1966) distance measure and the Neyman-Pearson variant of the decentralized detection problem

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Communications, IEEE Transactions on  (Volume:41 ,  Issue: 4 )