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Abstract: This paper investigates the effect of quantization on the performance of theNeyman-Pearson test. It is assumed that a sensing unit observes samples of acorrelated stationary ergodic multivariate process. Each sample is passedthrough an N-point quantizer and transmitted to a decision device whichperforms a binary hypothesis test. For any false alarm level, it is shown thatthe miss probability of the Neyman-Pearson test converges to zero exponentiallyas the number of samples tends to infinity, assuming that the observed processsatisfies certain mixing conditions. The main contribution of this paper is toprovide a compact closed-form expression of the error exponent in the high-rateregime i.e., when the number N of quantization levels tends to infinity,generalizing previous results of Gupta and Hero to the case of non-independentobservations. If d represents the dimension of one sample, it is proved thatthe error exponent converges at rate N^{2-d} to the one obtained in the absenceof quantization. As an application, relevant high-rate quantization strategieswhich lead to a large error exponent are determined. Numerical results indicatethat the proposed quantization rule can yield better performance than existingones in terms of detection error.



Author: Joffrey Villard, Pascal Bianchi

Source: https://arxiv.org/







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