Rate vs. Covertness for the Packet Insertion Problem

The goal of covert communication is to establish a communication link between two parties (Alice and Bob) while assuring that a warden (Willie) will not be able to detect the very presence of communication. In this work, we address the covert communication problem over a packet insertion channel. Assuming a Poisson channel model, we first consider an all-Aware warden, who wishes to minimize the sum of his miss detection and false alarm probabilities. We show that the covertness extent versus Alice's transmission rate can be computed exactly. We also derive simplified bounds which are tighter than previously known results. Such a warden, however, has to be aware of Alice's transmission rate. A more practical scenario, is when the warden does not have this information, hence wishes to operate at a certain false alarm rate. For this case, we discuss Alice's strategy to ensure the warden's miss detection probability is lower bounded. Finally, we study covertness in the case where Willie has uncertainty regarding the nominal channel rate as well, and show that in this case, Alice's covert transmission rate can be even higher.