Distributed Detection over Random Networks: Large Deviations Performance Analysis

TL;DR

This paper analyzes the large deviations performance of distributed detection algorithms over random networks, revealing a phase change in error decay rates depending on the network information flow rate.

Contribution

It characterizes the exponential decay rate of error probability in distributed detection over random networks and identifies a threshold effect related to network information flow.

Findings

Above the threshold, detection is asymptotically optimal, matching centralized performance.

Below the threshold, detection achieves a fraction of the optimal Chernoff information rate.

Simulations confirm the theoretical phase change behavior.

Abstract

We study the large deviations performance, i.e., the exponential decay rate of the error probability, of distributed detection algorithms over random networks. At each time step $k$ each sensor: 1) averages its decision variable with the neighbors' decision variables; and 2) accounts on-the-fly for its new observation. We show that distributed detection exhibits a "phase change" behavior. When the rate of network information flow (the speed of averaging) is above a threshold, then distributed detection is asymptotically equivalent to the optimal centralized detection, i.e., the exponential decay rate of the error probability for distributed detection equals the Chernoff information. When the rate of information flow is below a threshold, distributed detection achieves only a fraction of the Chernoff information rate; we quantify this achievable rate as a function of the network rate of information flow. Simulation examples demonstrate our theoretical findings on the behavior of distributed detection over random networks.