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The two-user Gaussian interference channel (G-IC) is revisited, with aparticular focus on practically amenable discrete input signalling and treatinginterference as noise (TIN) receivers. The corresponding deterministicinterference channel (D-IC) is first investigated and coding schemes that canachieve the entire capacity region of D-IC under TIN are proposed. Theseschemes are then systematically translate into multi-layer superposition codingschemes based on purely discrete inputs for the real-valued G-IC. Our analysisshows that the proposed scheme is able to achieve the entire capacity region towithin 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 TINfor the entire capacity region and all the interference regimes. Furthermore,the approach is extended to obtain coding scheme based on discrete inputs forthe complex-valued G-IC. For such a scenario, the minimum distance and theachievable rate of the proposed scheme under TIN are analyzed, which takes intoaccount the effects of random phase rotations introduced by the channels.Simulation results show that our scheme is capable of approaching the capacityregion of the complex-valued G-IC and significantly outperforms Gaussiansignalling with TIN in various interference regimes.

Discrete Signaling and Treating Interference as Noise for the Gaussian Interference Channel