论文标题
高斯在扩大HK速率区域的最佳性，及其与2用户GIC的容量区域的重叠
Optimality of Gaussian in Enlarging HK Rate Region, and its Overlap with the Capacity Region of 2-users GIC
论文作者
论文摘要
本文表明，一组HK约束对应于在其SUP空间上投射两个多个访问通道的交集。香港约束的关键属性是，用户1（或用户2）的私人消息是对接收器2（或接收器1）形成的MAC的叠置编码的最后一层，并将在接收器2（或接收机1）的解码操作中被视为噪声。本文中使用了该属性，以表明，在基于加性高斯噪声模型的HK速率区域中，高斯分布最适合扩大该区域。众所周知，在干扰通道中可以实现HK速率区域。另一方面，参考文献[Khandani-arxiv：2011.12981]提出了一种基于无限步骤中容量区域的边界的2个用户弱GIC中代码书构造的方法。在[Khandani-arxiv：2011.12981]中构建的区域与HK速率区域中表面表面的相同两个多个访问通道的交点一致。参考文献[Khandani-arxiv：2011.12981]还表明，由于上述关键特性，2用户GIC容量区域不能超过HK速率区域。这意味着，使用高斯代码书，HK速率区域是最佳扩大的，并且相同的高斯代码书实现了2用户GIC的容量区域。
This article shows that the set of HK constraints correspond to projecting the intersection of two multiple access channels on its sup-spaces. A key property of HK constraints is that the private message of user 1 (or of user 2) is the last layer in superposition coding for the MAC formed at receiver 2 (or at receiver 1) and will be treated as noise in the decoding operations at receiver 2 (or at receiver 1). This property is used in this article to show that, in a HK rate region based on an additive Gaussian noise model, Gaussian distribution is optimum for enlarging the region. It is known that the HK rate region is achievable in an interference channel. On the other hand, reference [Khandani-arXiv:2011.12981] presents a method for code-book construction in a 2-users weak GIC, using Gaussian inputs, based on covering the boundary of the capacity region in infinitesimal steps. The region constructed in [Khandani-arXiv:2011.12981] coincides with the intersection of the same two multiple access channels that surface in the HK rate region. Reference [Khandani-arXiv:2011.12981] also shows that, due to the aforementioned key property, 2-users GIC capacity region cannot extend beyond the HK rate region. This means, using Gaussian code-books, the HK rate region is optimally enlarged and the same Gaussian code-books achieve the capacity region of the 2-users GIC.
