  This paper studies the effect of optimal power allocation on the performance
of communication systems utilizing automatic repeat request (ARQ). Considering
Type-I ARQ, the problem is cast as the minimization of the outage probability
subject to an average power constraint. The analysis is based on some recent
results on the achievable rates of finite-length codes and we investigate the
effect of codewords length on the performance of ARQ-based systems. We show
that the performance of ARQ protocols is (almost) insensitive to the length of
the codewords, for codewords of length $\ge 50$ channel uses. Also, optimal
power allocation improves the power efficiency of the ARQ-based systems
substantially. For instance, consider a Rayleigh fading channel, codewords of
rate 1 nats-per-channel-use and outage probability $10^{-3}.$ Then, with a
maximum of 2 and 3 transmissions, the implementation of power-adaptive ARQ
reduces the average power, compared to the open-loop communication setup, by 17
and 23 dB, respectively, a result which is (almost) independent of the
codewords length. Also, optimal power allocation increases the diversity gain
of the ARQ protocols considerably.
