  Link adaptation, in particular adaptive coded modulation (ACM), is a
promising tool for bandwidth-efficient transmission in a fading environment.
The main motivation behind employing ACM schemes is to improve the spectral
efficiency of wireless communication systems. In this paper, using a finite
number of capacity achieving component codes, we propose new transmission
schemes employing constant power transmission, as well as discrete and
continuous power adaptation, for slowly varying flat-fading channels.
  We show that the proposed transmission schemes can achieve throughputs close
to the Shannon limits of flat-fading channels using only a small number of
codes. Specifically, using a fully discrete scheme with just four codes, each
associated with four power levels, we achieve a spectral efficiency within 1 dB
of the continuous-rate continuous-power Shannon capacity. Furthermore, when
restricted to a fixed number of codes, the introduction of power adaptation has
significant gains with respect to ASE and probability of no transmission
compared to a constant power scheme.
