Reaching consensus on a binary state by exchanging binary actions

In this paper, we study the problem of distributed hypothesis testing in cooperative networks of agents. All agents are trying to reach consensus on the state of nature by their private signals and the binary actions of their neighbors. This is a challenging problem because the exchanged information of the agents is highly compressed. We propose a gossip-type method where every agent's decision converges in probability to the optimal decision held by a fictitious fusion center. We prove the asymptotical property of the proposed method and provide simulation results that demonstrate the communication cost and convergence time of the method.