What determines average and outage performance in fading channels?

We quantify the average performance of digital transmissions over fading channels at high signal-to-noise ratio (SNR). The performance criteria considered here are probability of error and outage probability. We show that as functions of the average SNR, they can both be characterized by two parameters: the diversity and coding gains. They have the same diversity order, but their coding gains in dB differ by a constant. The diversity and coding gains are found to be related to the behavior of the probability density function (PDF) only at the origin, or equivalently, to the decaying order of the characteristic function. Diversity and coding gains for diversity combining systems are found in terms of branch average SNR's for arbitrarily distributed independent (in some cases, correlated) branches, which can allow one to analyze, e.g., coded transmissions through independent or correlated fading channels.