  The two-user Gaussian interference channel (G-IC) is revisited, with a
particular focus on practically amenable discrete input signalling and treating
interference as noise (TIN) receivers. The corresponding deterministic
interference channel (D-IC) is first investigated and coding schemes that can
achieve the entire capacity region of D-IC under TIN are proposed. These
schemes are then systematically translate into multi-layer superposition coding
schemes based on purely discrete inputs for the real-valued G-IC. Our analysis
shows that the proposed scheme is able to achieve the entire capacity region to
within a constant gap for all channel parameters. To the best of our knowledge,
this is the first constant-gap result under purely discrete signalling and TIN
for the entire capacity region and all the interference regimes. Furthermore,
the approach is extended to obtain coding scheme based on discrete inputs for
the complex-valued G-IC. For such a scenario, the minimum distance and the
achievable rate of the proposed scheme under TIN are analyzed, which takes into
account the effects of random phase rotations introduced by the channels.
Simulation results show that our scheme is capable of approaching the capacity
region of the complex-valued G-IC and significantly outperforms Gaussian
signalling with TIN in various interference regimes.
