Covert Outage Minimization in the Presence of Multiple Wardens

The idea of covert communication is to conceal the presence of a transmission from an illegitimate receiver, known as a warden. This paper tackles the problem of finite blocklength covert communication in the presence of multiple colluding wardens. The system consists of Alice, who aims to covertly transmit to Bob with the help of a cooperative jammer (henceforth known as Jammer), and a Fusion Center (FC) in charge of combining the wardens' information and deciding on the presence of Alice's transmission accordingly. In our proposed approach, we utilize a two-player zero-sum game to model the interaction between Alice and Jammer jointly as one player and FC as the second player. In this game, Alice and Jammer cooperatively randomize over a range of transmitting and jamming powers to confuse FC. In contrast, FC randomly changes the detection threshold to confuse Alice. The main focus of the paper is to study the impact of employing multiple wardens on the trade-off between the probability of error at FC and the outage probability at Bob. We derive a pay-off function that can be efficiently computed using linear programming to find the optimal distributions of transmitting and jamming powers as well as thresholds used by FC. The benefit of using a cooperative jammer in neutralizing the advantage of employing multiple wardens is shown by analytical results and numerical simulations.