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The K-receiver wiretap channel is a channel model where a transmitterbroadcasts K independent messages to K intended receivers while keeping themsecret from an eavesdropper. The capacity region of the K-receivermultiple-input multiple-output (MIMO) wiretap channel has been characterized byusing dirty-paper coding and stochastic encoding. However, K factorial encodingorders may need to be enumerated to evaluate the capacity region, which makesthe problem intractable. In addition, even though the capacity region is known,the optimal signaling to achieve the capacity region is unknown. In this paper,we determine one optimal encoding order to achieve every point on the capacityregion, and thus reduce the encoding complexity K factorial times. We provethat the optimal decoding order for the K-receiver MIMO wiretap channel is thesame as that for the MIMO broadcast channel without secrecy. To be specific,the descending weight ordering in the weighted sum-rate (WSR) maximizationproblem determines the optimal encoding order. Next, to reach the border of thesecrecy capacity region, we form a WSR maximization problem and apply the blocksuccessive maximization method to solve this nonconvex problem and find theinput covariance matrices corresponding to each message. Numerical results areused to verify the optimality of the encoding order and to demonstrate theefficacy of the proposed signaling design.

K-Receiver Wiretap Channel: Optimal Encoding Order and Signaling Design