  This work proposes a novel outer bound for the Gaussian cognitive
interference channel in strong interference at the primary receiver based on
the capacity of a multi-antenna broadcast channel with degraded message set. It
then shows that for the Z-channel, i.e., when the secondary receiver
experiences no interference and the primary receiver experiences strong
interference, the proposed outer bound not only is the tightest among known
bounds but is actually achievable for sufficiently strong interference. The
latter is a novel capacity result that from numerical evaluations appears to be
generalizable to a larger (i.e., non-Z) class of Gaussian channels.
