  A coding scheme is proposed for the memoryless Gaussian broadcast channel
with correlated noises and feedback. For all noise correlations other than -1,
the gap between the sum-rate the scheme achieves and the full-cooperation bound
vanishes as the signal-to-noise ratio tends to infinity. When the correlation
coefficient is -1, the gains afforded by feedback are unbounded and the prelog
is doubled. When the correlation coefficient is +1 we demonstrate a dichotomy:
If the noise variances are equal, then feedback is useless, and otherwise,
feedback affords unbounded rate gains and doubles the prelog. The unbounded
feedback gains, however, require perfect (noiseless) feedback. When the
feedback links are noisy the feedback gains are bounded, unless the feedback
noise decays to zero sufficiently fast with the signal-to-noise ratio.
Extensions to more receivers are also discussed as is the memoryless Gaussian
interference channel with feedback.
