  This paper investigates the maximal channel coding rate achievable at a given
blocklength $n$ and error probability $\epsilon$, when the codewords are
subject to a long-term (i.e., averaged-over-all-codeword) power constraint. The
second-order term in the large-$n$ expansion of the maximal channel coding rate
is characterized both for additive white Gaussian noise (AWGN) channels and for
quasi-static fading channels with perfect channel state information available
at both the transmitter and the receiver. It is shown that in both cases the
second-order term is proportional to $\sqrt{n^{-1}\ln n}$. For the quasi-static
fading case, this second-order term is achieved by truncated channel inversion,
namely, by concatenating a dispersion-optimal code for an AWGN channel subject
to a short-term power constraint, with a power controller that inverts the
channel whenever the fading gain is above a certain threshold. Easy-to-evaluate
approximations of the maximal channel coding rate are developed for both the
AWGN and the quasi-static fading case.
