Covert Communication Over a $K$ -User Multiple-Access Channel

We consider a scenario in which <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> transmitters attempt to communicate covert messages reliably to a legitimate receiver over a discrete memoryless multiple-access channel (MAC) while simultaneously escaping detection from an adversary who observes their communication through another discrete memoryless MAC. We assume that each transmitter may use a secret key that is shared only between itself and the legitimate receiver. We show that each of the <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> transmitters can transmit on the order of <inline-formula> <tex-math notation="LaTeX">$\sqrt {n}$ </tex-math></inline-formula> reliable and covert bits per <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> channel uses, exceeding which, the warden will be able to detect the communication. We identify the optimal pre-constants of the scaling, which leads to a complete characterization of the covert capacity region of the <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-user binary-input MAC. We show that, asymptotically, all sum-rate constraints are inactive unlike the traditional MAC capacity region. We also characterize the channel conditions that have to be satisfied for the transmitters to operate without a secret key.