We study the compound multi-input multi-output (MIMO) broadcast channel with
confidential messages (BCC), where one transmitter sends a common message to
two receivers and two confidential messages respectively to each receiver. The
channel state may take one of a finite set of states, and the transmitter knows
the state set but does not know the realization of the state. We study
achievable rates with perfect secrecy in the high SNR regime by characterizing
an achievable secrecy degree of freedom (s.d.o.f.) region for two models, the
Gaussian MIMO-BCC and the ergodic fading multi-input single-output (MISO)-BCC
without a common message. We show that by exploiting an additional temporal
dimension due to state variation in the ergodic fading model, the achievable
s.d.o.f. region can be significantly improved compared to the Gaussian model
with a constant state, although at the price of a larger delay.Comment: To appear in Proc. IEEE Symposium on Information Theory (ISIT 2009)
June 28 - July 3, 2009, Seoul, Kore