  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 m times the Singleton bound. We also illustrate the significant gains
available by employing long-term power constraints. In particular, we analyze
the optimal long-term solution, showing that zero outage can be achieved
provided that the corresponding short-term SNR exponent with the same system
parameters is strictly greater than one. Conversely, if the short-term SNR
exponent is smaller than one, we show that zero outage cannot be achieved. In
this case, we derive the corresponding long-term SNR exponent as a function of
the Singleton bound. Due to the nature of the expressions involved, the
complexity of optimal schemes may be prohibitive for system implementation. We
therefore propose simple sub-optimal power allocation schemes whose outage
probability performance is very close to the minimum outage probability
obtained by optimal schemes. We also show the applicability of these techniques
to practical systems employing orthogonal frequency division multiplexing.
