  We study the best exponential decay in the blocklength of the probability of
error that can be achieved in the transmission of a single bit over the
Gaussian channel with an active noisy Gaussian feedback link. We impose an
\emph{expected} block power constraint on the forward link and study both
\emph{almost-sure} and \emph{expected} block power constraints on the feedback
link. In both cases the best achievable error exponents are finite and grow
approximately proportionally to the larger between the signal-to-noise ratios
on the forward and feedback links. The error exponents under almost-sure block
power constraints are typically strictly smaller than under expected
constraints. Some of the results extend to communication at arbitrary rates
below capacity and to general discrete memoryless channels.
