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We extend previous results on covert communication over the additive whiteGaussian noise channel to two other types of additive noise channels. The firstis the Gaussian channel with memory, where the noise sequence is a Gaussianvector with an arbitrary invertible covariance matrix. We show that thefundamental limit for covert communication over such a channel is the same asover the channel with white, i.e., memoryless, Gaussian noise. The second typeof channel we consider is one with memoryless generalized Gaussian noise. Forsuch a channel we prove a general upper bound on the dominant term in themaximum number of nats that can be covertly communicated over n channel uses.When the shape parameter p of the generalized Gaussian noise distribution is inthe interval (0, 1], we also prove a matching lower bound.

Covert Communication over Two Types of Additive Noise Channels