  We consider data transmission across discrete memoryless channels (DMCs)
using variable-length codes with feedback. We consider the family of such codes
whose rates are $\rho_N$ below the channel capacity $C$, where $\rho_N$ is a
positive sequence that tends to zero slower than the reciprocal of the square
root of the expectation of the (random) blocklength $N$. This is known as the
moderate deviations regime and we establish the optimal moderate deviations
constant. We show that in this scenario, the error probability decays
sub-exponentially with speed $\exp(-(B/C)N\rho_N)$, where $B$ is the maximum
relative entropy between output distributions of the DMC.
