  We consider power allocation algorithms for fixed-rate transmission over
Nakagami-m non-ergodic block-fading channels with perfect transmitter and
receiver channel state information and discrete input signal constellations
under both short- and long-term power constraints. Optimal power allocation
schemes are shown to be direct applications of previous results in the
literature. We show that the SNR exponent of the optimal short-term scheme is
given by the Singleton bound. We also illustrate the significant gains
available by employing long-term power constraints. Due to the nature of the
expressions involved, the complexity of optimal schemes may be prohibitive for
system implementation. We propose simple sub-optimal power allocation schemes
whose outage probability performance is very close to the minimum outage
probability obtained by optimal schemes.
