Optimal Point-to-Point Codes in Interference Channels: An Incremental I-MMSE approach

A recent result of the authors shows a so-called I-MMSE-like relationship that, for the two-user Gaussian interference channel, an I-MMSE relationship holds in the limit, as n $\to \infty$, between the interference and the interfered-with receiver, assuming that the interfered-with transmission is an optimal point-to-point sequence (achieves the point-to-point capacity). This result was further used to provide a proof of the "missing corner points" of the two-user Gaussian interference channel. This paper provides an information theoretic proof of the above-mentioned I-MMSE-like relationship which follows the incremental channel approach, an approach which was used by Guo, Shamai and Verd\'u to provide an insightful proof of the original I-MMSE relationship for point-to-point channels. Finally, some additional applications of this result are shown for other multi-user settings: the Gaussian multiple-access channel with interference and specific K-user Gaussian Z-interference channel settings.