  Achievable error exponents for the one-way with noisy feedback and two-way
AWGN channels are derived for the transmission of a finite number of messages
$M$ using fixed block length $n$, under the almost sure (AS) and the expected
block (EXP) power constraints. In the one-way setting under noisy AWGN
feedback, it is shown that under the AS constraint and when the feedback link
is much stronger than the direct link, active feedback leads to a larger gain
over the non-feedback error exponent than passive feedback. Under the EXP
constraint, a previously known error exponent for the transmission of two
messages is generalized to any arbitrary but finite number of messages $M$.
  In the two-way setting, where each user has its own message to send in
addition to (possibly) aiding in the transmission of feedback for the opposite
direction, error exponent regions are defined and derived for the first time
for the AWGN two-way channel under both AS and EXP power constraints. It is
shown that feedback or interaction may lead to error exponent gains in one
direction, possibly at the expense of a decrease in the error exponents
attained in the other direction. The relationship between $M$ and $n$ supported
by our achievability strategies is explored.
