Extremal properties of likelihood-ratio quantizers

The paper concerns a situation in which there are M hypotheses H/sub 1/,. . ., H/sub M/, and in which Y is a random variable taking values in a set Y', with a different probability distribution under each hypothesis. A quantizer gamma :Y' to (1,. . ., D) is applied to form a quantized random variable gamma (Y). The extreme points of the set of possible probability distributions of gamma (Y) are characterized as gamma ranges over all quantizers. Optimality properties of likelihood-ratio quantizers are then established for a very broad class of quantization problems, including problems involving the maximization of a distance measure as discussed by S.M. Ali and S.D. Silvey(1966).<<ETX>>

[1]  J. Wolfowitz,et al.  Relations among certain ranges of vector measures , 1951 .

[2]  H. Chernoff.  A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations , 1952 .

[3]  S. M. Ali,et al.  A General Class of Coefficients of Divergence of One Distribution from Another , 1966 .

[4]  H. V. Poor,et al.  Applications of Ali-Silvey Distance Measures in the Design of Generalized Quantizers for Binary Decision Systems , 1977, IEEE Trans. Commun..

[5]  Saleem A. Kassam,et al.  Optimum Quantization for Signal Detection , 1977, IEEE Trans. Commun..

[6]  Nils Sandell,et al.  Detection with Distributed Sensors , 1980, IEEE Transactions on Aerospace and Electronic Systems.

[7]  L. Ekchian,et al.  Detection networks , 1982, 1982 21st IEEE Conference on Decision and Control.

[8]  H. Vincent Poor,et al.  On Optimum and Nearly Optimum Data Quantization for Signal Detection , 1984, IEEE Trans. Commun..

[9]  R. Srinivasan.  Distributed radar detection theory , 1986 .

[10]  Imad Hoballah,et al.  Neyman-Pearson detection wirh distributed sensors , 1986, 1986 25th IEEE Conference on Decision and Control.

[11]  R. Srinivasan.  A theory of distributed detection , 1986 .

[12]  Ramanarayanan Viswanathan,et al.  Optimal Decision Fusion in Multiple Sensor Systems , 1987, IEEE Transactions on Aerospace and Electronic Systems.

[13]  Robert M. Gray,et al.  Encoding of correlated observations , 1987, IEEE Trans. Inf. Theory.

[14]  H. Poor,et al.  Fine quantization in signal detection and estimation , 1988, IEEE Trans. Inf. Theory.

[15]  Patrick Duvaut,et al.  Optimum quantization for detection , 1988, IEEE Trans. Commun..

[16]  John N. Tsitsiklis,et al.  Decentralized detection by a large number of sensors , 1988, Math. Control. Signals Syst..

[17]  Michael C. Wicks,et al.  Advances in signal detection for distributed multisensor data , 1989, Conference Proceedings., IEEE International Conference on Systems, Man and Cybernetics.

[18]  D. Warren,et al.  Optimal Decentralized Detection for Conditionally Independent Sensors , 1989, 1989 American Control Conference.

[19]  M. Barkat,et al.  Decentralized CFAR signal detection , 1989 .

[20]  Gerald R. Benitz,et al.  Asymptotically optimal quantizers for detection of I.I.D. data , 1989, IEEE Trans. Inf. Theory.