Secrecy capacity region of the degraded compound multi-receiver wiretap channel

We study the degraded compound multi-receiver wiretap channel, which consists of two groups of users and a group of eavesdroppers. We consider two different communication scenarios. In both scenarios, the transmitter sends two confidential messages, one for each group of users. In the first scenario, 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 multi-input multi-output (MIMO) channel model, we obtain the secrecy capacity region when there is only one user in the second group. In the second scenario, the message sent to the first group of users needs to be kept confidential from both the second group of users and eavesdroppers, whereas the message sent to the second group of users needs to be kept confidential only from the eavesdroppers. For this scenario, we do not put any restriction on the number of eavesdroppers. We find 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 obtain the secrecy capacity region when there is only one user in the second group.