  Transmitter channel state information (CSIT) is crucial for the multiplexing
gains offered by advanced interference management techniques such as multiuser
MIMO and interference alignment. Such CSIT is usually obtained by feedback from
the receivers, but the feedback is subject to delays. The usual approach is to
use the fed back information to predict the current channel state and then
apply a scheme designed assuming perfect CSIT. When the feedback delay is large
compared to the channel coherence time, such a prediction approach completely
fails to achieve any multiplexing gain. In this paper, we show that even in
this case, the completely stale CSI is still very useful. More concretely, we
show that in a MIMO broadcast channel with $K$ transmit antennas and $K$
receivers each with 1 receive antenna, $\frac{K}{1+1/2+ ...+ \frac{1}{K}} (> 1)
$ degrees of freedom is achievable even when the fed back channel state is
completely independent of the current channel state. Moreover, we establish
that if all receivers have independent and identically distributed channels,
then this is the optimal number of degrees of freedom achievable. In the
optimal scheme, the transmitter uses the fed back CSI to learn the side
information that the receivers receive from previous transmissions rather than
to predict the current channel state. Our result can be viewed as the first
example of feedback providing a degree-of-freedom gain in memoryless channels.
