i.i.d. Mixed Inputs and Treating Interference as Noise are gDoF Optimal for the Symmetric Gaussian Two-user Interference Channel

While a multi-letter limiting expression of the capacity region of the two-user Gaussian interference channel is known, capacity is generally considered to be open as this is not computable. Other computable capacity outer bounds are known to be achievable to within 1/2 bit using Gaussian inputs and joint decoding in the simplified Han and Kobayashi (single-letter) achievable rate region. This work shows that the simple scheme known as "treating interference as noise" without time-sharing attains the capacity region outer bound of the symmetric Gaussian interference channel to within either a constant gap, or a gap of order O(log log (SNR)), for all parameter regimes. The scheme is therefore optimal in the generalized Degrees of Freedom (gDoF) region sense almost surely. The achievability is obtained by using i.i.d. mixed inputs (i.e., a superposition of discrete and Gaussian random variables) in the multi-letter capacity expression, where the optimal number of points in the discrete part of the inputs, as well as the optimal power split among the discrete and continuous parts of the inputs, are characterized in closed form. An important practical implication of this result is that the discrete part of the inputs behaves as a "common message" whose contribution can be removed from the channel output, even though joint decoding is not employed. Moreover, time-sharing may be mimicked by varying the number of points in the discrete part of the inputs.