  This paper considers the problem of secret communication over a two-receiver
multiple-input multiple-output (MIMO) Gaussian broadcast channel. The
transmitter has two independent messages, each of which is intended for one of
the receivers but needs to be kept asymptotically perfectly secret from the
other. It is shown that, surprisingly, under a matrix power constraint both
messages can be simultaneously transmitted at their respective maximal secrecy
rates. To prove this result, the MIMO Gaussian wiretap channel is revisited and
a new characterization of its secrecy capacity is provided via a new coding
scheme that uses artificial noise and random binning.
