  This paper shows that for the two-user Gaussian Interference Channel (G-IC)
Treating Interference as Noise without Time Sharing (TINnoTS) achieves the
closure of the capacity region to within either a constant gap, or to within a
gap of the order O(logln(min(S,I))) where S is the largest Signal to Noise
Ratio (SNR) on the direct links and I is the largest Interference to Noise
Ratio (INR) on the cross links. As a consequence, TINnoTS is optimal from a
generalized Degrees of Freedom (gDoF) perspective for all channel gains except
for a subset of zero measure. TINnoTS with Gaussian inputs is known to be
optimal to within 1/2 bit for a subset of the weak interference regime.
Surprisingly, this paper shows that TINnoTS is gDoG optimal in all parameter
regimes, even in the strong and very strong interference regimes where joint
decoding of Gaussian inputs is optimal. For approximate optimality of TINnoTS
in all parameter regimes it is critical to use non-Gaussian inputs. This work
thus proposes to use mixed inputs as channel inputs where a mixed input is the
sum of a discrete and a Gaussian random variable. Interestingly, compared to
the Han-Kobayashi inner bound, the discrete part of a mixed input is shown to
effectively act as a common message in the sense that, although treated as
noise, its effect on the achievable rate region is as if it were jointly
decoded together with the desired messages at a non-intended receiver. The
practical implication is that a discrete interfering input is a 'friend', while
a Gaussian interfering input is in general a 'foe'. Since TINnoTS requires
neither joint decoding nor time sharing, the results of this paper are
applicable to a variety of oblivions or asynchronous channels, such as the
block asynchronous G-IC (which is not an information stable) and the G-IC with
partial codebook knowledge at one or more receivers.
