  We study asymptotic performance of distributed detection in large scale
connected sensor networks. Contrasting to the canonical parallel network 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 Neyman-Pearson 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.
