  A generic intuition says that the pre-log, or multiplexing gain, cannot be
larger than the minimum of the number of transmit and receive dimensions. This
suggests that for the scalar broadcast channel, the pre-log cannot exceed one.
By contrast, in this note, we show that when the noises are anti-correlated and
feedback is present, then a pre-log of two can be attained. In other words, in
this special case, in the limit of high SNR, the scalar Gaussian broadcast
channel turns into two parallel AWGN channels. Achievability is established via
a coding strategy due to Schalkwijk, Kailath, and Ozarow.
