Nearly optimal non-Gaussian codes for the Gaussian interference channel

Recent work demonstrated that for the two-user Gaussian Interference Channel (G-IC) sub-optimal point-to-point codes can outperform optimal (Gaussian) point-to-point codes. However, it is not clear how far from capacity such sub-optimal codes operate. This work demonstrates a family of sub-optimal codes, generated from a mixture of Gaussian and discrete random variables, that is optimal up to an additive gap for the G-IC. The developed tools are of interest on their own and can be used in a variety of channel models. For example, it can be shown that the capacity of the block-asynchronous G-IC where the decoders are prevented from decoding the interfering signals is to within an additive gap of the capacity of the classical G-IC where the receivers are fully synchronized and informed about the interfering codebooks.