  We show that $T$ rounds of interaction over the binary symmetric channel
$BSC_{1/2-\epsilon}$ with feedback can be simulated with $O(\epsilon^2 T)$
rounds of interaction over a noiseless channel. We also introduce a more
general "energy cost" model of interaction over a noisy channel. We show energy
cost to be equivalent to external information complexity, which implies that
our simulation results are unlikely to carry over to energy complexity. Our
main technical innovation is a self-reduction from simulating a noisy channel
to simulating a slightly-less-noisy channel, which may have other applications
in the area of interactive compression.
