High-Rate Quantization for the Neyman-Pearson Detection of Hidden Markov Processes

This paper investigates the decentralized detection of Hidden Markov Processes using the NeymanPearson test. We consider a network formed by a large number of distributed sensors. Sensors' observations are noisy snapshots of a Markov process to be detected. Each (real) observation is quantized on log2(N) bits before being transmitted to a fusion center which makes the final decision. 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 sensors tends to infinity. The error exponent is provided using recent results on Hidden Markov Models. In order to obtain informative expressions of the error exponent as a function of the quantization rule, we further investigate the case where the number N of quantization levels tends to infinity, following the approach developed in [1]. In this regime, we provide the quantization rule maximizing the error exponent. Illustration of our results is provided in ...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Joffrey Villard, Pascal Bianchi, Eric Moulines, Pablo Piantanida
• Keywords: CORR 2010, Education, Error Exponent, Quantization Rule, Sensors