  The Gaussian multiple-input multiple-output (MIMO) multi-receiver wiretap
channel is studied in this paper. The base station broadcasts confidential
messages to K intended users while keeping the messages secret from an
eavesdropper. The capacity of this channel has already been characterized by
applying dirty-paper coding and stochastic encoding. However, K factorial
encoding orders may need to be enumerated for that, which makes the problem
intractable. We prove that there exists one optimal encoding order and reduced
the K factorial times to a one-time encoding. The optimal encoding order is
proved by forming a secrecy weighted sum rate (WSR) maximization problem. The
optimal order is the same as that for the MIMO broadcast channel without
secrecy constraint, that is, the weight of users' rate in the WSR maximization
problem determines the optimal encoding order. Numerical results verify the
optimal encoding order.
