  This paper derives high-SNR asymptotic average error rates over fading
channels by relating them to the outage probability, under mild assumptions.
The analysis is based on the Tauberian theorem for Laplace-Stieltjes transforms
which is grounded on the notion of regular variation, and applies to a wider
range of channel distributions than existing approaches. The theory of regular
variation is argued to be the proper mathematical framework for finding
sufficient and necessary conditions for outage events to dominate high-SNR
error rate performance. It is proved that the diversity order being $d$ and the
cumulative distribution function (CDF) of the channel power gain having
variation exponent $d$ at 0 imply each other, provided that the instantaneous
error rate is upper-bounded by an exponential function of the instantaneous
SNR. High-SNR asymptotic average error rates are derived for specific
instantaneous error rates. Compared to existing approaches in the literature,
the asymptotic expressions are related to the channel distribution in a much
simpler manner herein, and related with outage more intuitively. The high-SNR
asymptotic error rate is also characterized under diversity combining schemes
with the channel power gain of each branch having a regularly varying CDF.
Numerical results are shown to corroborate our theoretical analysis.
