Design of Binary Quantizers for Distributed Detection Under Secrecy Constraints

In this paper, we investigate the design of distributed detection networks in the presence of an eavesdropper (Eve). We consider the problem of designing binary sensor quantizers that maximize the Kullback-Leibler (KL) divergence at the fusion center (FC), when subject to a tolerable constraint on the KL divergence at Eve. We assume that the channels between the sensors and the FC (likewise the channels between the sensors and the Eve) are modeled as binary symmetric channels (BSCs). In the case of i.i.d. received symbols at both the FC and Eve, we prove that the structure of the optimal binary quantizers is a likelihood ratio test (LRT). We also present an algorithm to find the threshold of the optimal LRT, and illustrate it for the case of Additive white Gaussian noise (AWGN) observation models at the sensors. In the case of non-i.i.d. received symbols at both FC and Eve, we propose a dynamic-programming based algorithm to find efficient quantizers at the sensors. Numerical results are presented to illustrate the performance of the proposed network.