Sparse Regression Codes for Covert Communication over Multiple Access Channels

We study a covert multiple access channel (MAC) with two users. Specifically, each user aims to transmit a message through a noisy channel with a low probability of detection by the adversary. We propose two coding schemes based on sparse regression codes (SPARC), with either a joint approximate message passing (JAMP) decoder or a successive interference cancellation-AMP (SIC-AMP) decoder. Furthermore, we derive an upper bound for the transmission power with given noise power under covert constraint and perform several simulations. The results show that our schemes not only have near-optimal performance and low complexity under Gaussian noise but also perform consistently under other noise distributions.