Distributed Detection in Ad Hoc Networks Through Quantized Consensus-Part II: Asymptotically Optimal Detection via One-Bit Communications

We study asymptotic performance of distributed detection in large scale connected sensor networks. Contrasting to canonical parallel networks where a single node has access to local decisions from all other nodes, each node can only exchange information with its direct neighbors in the present setting. We establish that, with each node employing an identical one-bit quantizer for local information exchange, a novel consensus reaching approach can achieve the optimal asymptotic performance of centralized detection as the network size scales. The statement is true under three different detection frameworks: the Bayesian criterion where the maximum a posteriori detector is optimal, the Neyman-Pearson criterion with a constant type-I error probability constraint, and the NeymanPearson criterion with an exponential type-I error probability constraint. Leveraging recent development in distributed consensus reaching using bounded quantizers with possibly unbounded data (which are log-likelihood ratios of local observations in the context of distributed detection), we design a one-bit deterministic quantizer with controllable threshold that leads to desirable consensus error bounds. The obtained bounds are key to establishing the optimal asymptotic detection performance. In addition, we examine non-asymptotic performance of the proposed approach and show that the type-I and type-II error probabilities at each node can be made arbitrarily close to the centralized ones simultaneously when a continuity condition is satisfied. Index Terms Distributed detection, error exponent, one-bit quantizer, quantized consensus, large deviations.