2010/04/30 by Joffrey Villard, Pascal Bianchi · 5 citations
Computer Science · Decision Sciences · Mathematics · #Advanced Statistical Process Monitoring #Algorithm #Combinatorics #Discrete mathematics #Distributed Sensor Networks and Detection Algorithms #Ergodic theory #Mathematical analysis #Mathematics #Quantization (signal processing) #Statistical Methods and Inference #Statistics #cs.IT #math.IT #math.PR #math.ST #stat.TH
paper · pdf · doi:10.1109/tit.2011.2158479
published in IEEE Transactions on Information Theory 57(8), 5387-5409 (Institute of Electrical and Electronics Engineers) · 47 pages, 7 figures, 1 table. To appear in the IEEE Transactions on Information Theory
arxiv created 2011/05/04 · openalex publication_date 2011/08/01 · arxiv updated 2011/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This paper investigates the effect of quantization on the performance of the Neyman-Pearson test. It is assumed that a sensing unit observes samples of a correlated stationary ergodic multivariate process. Each sample is passed through anN-point quantizer and transmitted to a decision device which performs a binary hypothesis test. For any false alarm level, it is shown that the miss probability of the Neyman-Pearson test converges to zero exponentially as the number of samples tends to infinity, assuming that the observed process satisfies certain mixing conditions. The main contribution of this paper is to provide a compact closed-form expression of the error exponent in the high-rate regime, i.e., when the numberNof quantization levels tends to infinity, generalizing previous results of Gupta and Hero to the case of nonindependent observations. Ifdrepresents the dimension of one sample, it is proved that the error exponent converges at rateN2/dto the one obtained in the absence of quantization. As an application, relevant high-rate quantization strategies which lead to a large error exponent are determined. Numerical results indicate that the proposed quantization rule can yield better performance than existing ones in terms of detection error.