arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2011.12981cs.ITmath.IT
收藏

两用户弱高斯干扰信道的容量域

Capacity Region of Two-users Weak Gaussian Interference Channel

Amir K. Khandani

摘要:

高斯干扰信道(GIC)的计算容量是复杂的,因为需要输入分布的知识来找到封闭形式的互信息项,这应该在输入分布和相关联的资源分配上被优化。最佳解决方案可能需要在几个GIC(下文中,每个称为"组成区域")之间划分可用资源,并在它们之间应用分时。当前的文章重点讨论了一个2用户弱GIC的单个组成区域(意味着资源约束都满足等式)。它示出,通过依赖于一个不同的,直观地简单,解释的基本优化问题,可以确定的编码/解码策略的过程中计算的最佳解决方案。这是基于以无限小的步骤沿着容量区域的边界逐渐移动,其中每个步骤中的终点的解依赖于步骤的起点处的解而被优化。这种方法能够证明高斯分布在整个边界上是最优的,并且还允许找到描述容量区域的不同部分的简单封闭形式的解决方案。每个组成2用户GIC的解与Han Kobayashi(HK)约束系统的最优解一致,i.i.d.(标量)高斯输入。虽然本文的研究重点是2用户弱GIC,但高斯分布最优性的证明与交叉增益的大小无关,因此对强干扰信道、混合干扰信道、Z干扰信道以及两个以上用户的GIC都是普遍适用的。此外,通过重新推导假设交叉增益小于1而建立的各种条件,用于构造边界的过程适用于任意交叉增益值。

英文摘要:

Computing capacity of Gaussian Interference Channel (GIC) is complex since knowledge of input distributions is needed to find the mutual information terms in closed forms, which should be optimized over input distributions and associated resource allocation. The optimum solution may require dividing the available resources among several GIC (each called a "constituent region", hereafter) and apply time-sharing among them. The current article focuses on a single constituent region (meaning the constraints on resources are all satisfied with equality) for a 2-users weak GIC. It is shown that, by relying on a different, intuitively straightforward, interpretation of the underlying optimization problem, one can determine the encoding/decoding strategies in the process of computing the optimum solution. This is based on gradually moving along the boundary of the capacity region in infinitesimal steps, where the solution for the end point in each step is optimized relying on the solution at the step's starting point. This approach enables proving Gaussian distribution is optimum over the entire boundary, and also allows finding simple closed form solutions describing different parts of the capacity region. The solution for each constituent 2-users GIC coincides with the optimum solution to the Han Kobayashi (HK) system of constraints with i.i.d. (scalar) Gaussian inputs. Although the article is focused on 2-users weak GIC, the proof for optimality of Gaussian distribution is independent of the values of cross gains, and thereby is universally applicable to strong, mixed and Z interference channels, as well as to GIC with more than two users. In addition, the procedure for the construction of boundary is applicable for arbitrary cross gain values, by re-deriving various conditions that have been established assuming cross gains being less than one.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑