  This letter establishes a unified analytical framework to study the
asymptotic average mutual information (AMI) of mixture gamma (MG) distributed
fading channels driven by finite input signals in the high signal-to-noise
ratio (SNR) regime. It is found that the AMI converges to some constant as the
average SNR increases and its rate of convergence (ROC) is determined by the
coding gain and diversity order. Moreover, the derived results are used to
investigate the asymptotic optimal power allocation policy of a bank of
parallel fading channels having finite inputs. It is suggested that in the high
SNR region, the sub-channel with a lower coding gain or diversity order should
be allocated with more power. Finally, numerical results are provided to
collaborate the theoretical analyses.
