On the Optimality of Gaussian Code-books for Signaling over a Two-Users Weak Gaussian Interference Channel

This article shows that the capacity region of a two users weak Gaussian interference channel can be achieved using single letter Gaussian code-books. The approach relies on traversing the boundary in incremental steps. Starting from a corner point with Gaussian code-books, and relying on calculus of variation, it is shown that the end point in each step is achieved using Gaussian code-books. Optimality of Gaussian code-books is first established by limiting the random coding to independent and identically distributed scalar (single-letter) samples. Then, it is shown that the value of any optimum solution for vector inputs does not exceed that of the single-letter case. It is also shown that the maximum number of phases needed to realize the optimum time-sharing is two. It is established that the solution to the Han-Kobayashi achievable rate region, with single letter Gaussian code-books, achieves the optimum boundary. Even though the article focuses on weak interference, the results are applicable to the general case.