Constant Scaling Asymptotics of Communication Bounds in Covert Channels Against Selective Adversary

In the existing works on asymptotics of throughput of covert communications, an adversary is typically assumed to run a single binary hypothesis testing to determine the presence of active transmission, which is equivalent to distinguish between an induced mixture distribution by all codewords and the distribution with an inactive transmitter. In this paper, we show that both of the first and second order asymptotics are O(1) when the adversary can afford running parallel simple binary hypothesis testing against detection of each single codeword. The covert constraint in this case is given as an upper-bound δ on the total variation distance (TVD) between the simple distribution induced by each codeword and the one of pure noise. The result is drastically different in a negative way than the commonly known Square Root Law for covert communication over AWGN channels with a more benign adversary.