  The paper establishes the capacity region of the Gaussian interference
channel with many transmitter-receiver pairs constrained to use point-to-point
codes. The capacity region is shown to be strictly larger in general than the
achievable rate regions when treating interference as noise, using successive
interference cancellation decoding, and using joint decoding. The gains in
coverage and achievable rate using the optimal decoder are analyzed in terms of
ensemble averages using stochastic geometry. In a spatial network where the
nodes are distributed according to a Poisson point process and the channel path
loss exponent is $\beta > 2$, it is shown that the density of users that can be
supported by treating interference as noise can scale no faster than
$B^{2/\beta}$ as the bandwidth $B$ grows, while the density of users can scale
linearly with $B$ under optimal decoding.
