  We develop a characterization of fading models, which assigns a number called
logarithmic Jensen's gap to a given fading model. We show that as a consequence
of a finite logarithmic Jensen's gap, approximate capacity region can be
obtained for fast fading interference channels (FF-IC) for several scenarios.
We illustrate three instances where a constant capacity gap can be obtained as
a function of the logarithmic Jensen's gap. Firstly for an FF-IC with neither
feedback nor instantaneous channel state information at transmitter (CSIT), if
the fading distribution has finite logarithmic Jensen's gap, we show that a
rate-splitting scheme based on average interference-to-noise ratio (inr) can
achieve its approximate capacity. Secondly we show that a similar scheme can
achieve the approximate capacity of FF-IC with feedback and delayed CSIT, if
the fading distribution has finite logarithmic Jensen's gap. Thirdly, when this
condition holds, we show that point-to-point codes can achieve approximate
capacity for a class of FF-IC with feedback. We prove that the logarithmic
Jensen's gap is finite for common fading models, including Rayleigh and
Nakagami fading, thereby obtaining the approximate capacity region of FF-IC
with these fading models. For Rayleigh fading the capacity gap is obtained as
1.83 bits per channel use for non-feedback case and 2.83 bits per channel use
for feedback case. Our analysis also yields approximate capacity results for
fading 2-tap ISI channel and fading interference multiple access channel as
corollaries.
