MIMO Gaussian broadcast channels with common, private and confidential messages

Z. Goldfeld

In Proceedings of the 2016 IEEE Information Theory Workshop (ITW-2016), Cambridge, UK, September 2016

The two-user multiple-input multiple-output
(MIMO) Gaussian broadcast channel (BC) with common,
private and confidential messages is considered. The transmitter
sends a common message to both users, a confidential message
to User 1 and a private (non-confidential) message to User
2. The secrecy-capacity region is characterized by showing
that certain inner and outer bounds coincide and that the
boundary points are achieved by Gaussian inputs. The proof
relies on factorization of upper concave envelopes and a variant
of dirty-paper coding (DPC). The entire region is exhausted
by using DPC to cancel out the signal of the non-confidential
message at Receiver 1, making DPC against the signal of the
confidential message unnecessary. The secrecy-capacity results
are visualized using a numerical example.