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

TL;DR

This paper studies decentralized detection of Hidden Markov Processes with quantized sensor data, showing that error probability decreases exponentially with more sensors and optimizing quantization for best detection performance.

Contribution

It introduces a quantization rule that maximizes the error exponent in Neyman-Pearson detection of Hidden Markov Processes, extending previous results to the quantization setting.

Findings

Error probability decreases exponentially with the number of sensors.

Optimized quantization rule outperforms previous methods for i.i.d. observations.

Provides explicit error exponent expressions as a function of quantization levels.

Abstract

This paper investigates the decentralized detection of Hidden Markov Processes using the Neyman-Pearson 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 [Gupta & Hero, 2003]. In this regime, we provide the quantization rule maximizing the error exponent. Illustration of our results is provided in the case of the detection of a Gauss-Markov signal in noise. In terms of error exponent, the proposed quantization rule significantly outperforms the one proposed by [Gupta & Hero, 2003] for i.i.d. observations.