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.

翻译：本文证明了弱高斯干扰信道双用户系统的容量域可通过单字母高斯码本实现。该方法基于边界逐步遍历：从高斯码本的角点出发，利用变分法证明每一步的终点均通过高斯码本达成。首先通过将随机编码限制为独立同分布标量（单字母）样本，确立了高斯码本的最优性。随后证明向量输入的任何最优解值均不超过单字母情形。研究还表明，实现最优时分复用最多仅需两个相位。本文证实了采用单字母高斯码本的Han-Kobayashi可达速率域解能够达到最优边界。尽管研究聚焦于弱干扰场景，所得结论同样适用于一般情况。