This article shows that the capacity region of a 2-users weak Gaussian interference channel is achieved using 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 optimum solution for vector inputs coincides with the single-letter case. It is also shown that the maximum number of phases needed to realize the gain due to power allocation over time is two. It is also established that the solution to the Han-Kobayashi achievable rate region, with single letter Gaussian random code-books, achieves the optimum boundary.

翻译：本文证明，双用户弱高斯干扰信道的容量区域可通过高斯码本实现。该方法基于逐步遍历边界的思想。从高斯码本对应的角点出发，利用变分法证明每一步的终点均可通过高斯码本实现。首先通过将随机编码限制为独立同分布的标量（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最优解与单字母情形一致。研究还表明，为实现时域功率分配增益所需的最大相位数为二。最后证实，采用单字母高斯随机码本的Han-Kobayashi可达速率区域解能够达到最优边界。