  In this paper, we study the degraded compound multi-receiver wiretap channel.
The degraded compound multi-receiver wiretap channel consists of two groups of
users and a group of eavesdroppers, where, if we pick an arbitrary user from
each group of users and an arbitrary eavesdropper, they satisfy a certain
Markov chain. We study two different communication scenarios for this channel.
In the first scenario, the transmitter wants to send a confidential message to
users in the first (stronger) group and a different confidential message to
users in the second (weaker) group, where both messages need to be kept
confidential from the eavesdroppers. For this scenario, we assume that there is
only one eavesdropper. We obtain the secrecy capacity region for the general
discrete memoryless channel model, the parallel channel model, and the Gaussian
parallel channel model. For the Gaussian multiple-input multiple-output (MIMO)
channel model, we obtain the secrecy capacity region when there is only one
user in the second group. In the second scenario we study, the transmitter
sends a confidential message to users in the first group which needs to be kept
confidential from the second group of users and the eavesdroppers. Furthermore,
the transmitter sends a different confidential message to users in the second
group which needs to be kept confidential only from the eavesdroppers. For this
scenario, we do not put any restriction on the number of eavesdroppers. As in
the first scenario, we obtain the secrecy capacity region for the general
discrete memoryless channel model, the parallel channel model, and the Gaussian
parallel channel model. For the Gaussian MIMO channel model, we establish the
secrecy capacity region when there is only one user in the second group.
