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