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.

翻译：我们将在加性高斯白噪声信道上的隐蔽通信现有结果扩展到另外两种加性噪声信道。第一种是具有记忆的高斯信道，其中噪声序列是具有任意可逆协方差矩阵的高斯向量。我们证明，在此类信道上进行隐蔽通信的基本极限与在白噪声（即无记忆高斯噪声）信道上的极限相同。我们考虑的第二种信道是无记忆广义高斯噪声信道。对于此类信道，我们证明了在n次信道使用中可隐蔽传输的最大奈特数主导项的一般上界。当广义高斯噪声分布的形状参数p位于区间(0,1]时，我们还证明了匹配的下界。