广播信道容量区域的Marton内界最优性分析

The broadcast channel is a classical model in network information theory, which models the downlink system of a communication scenario with one sender and multiple receivers. One of the fundamental problems is the capacity region, and the research focuses on the inner bounds and outer bounds. The first inner bound to the capacity region was given by superposition coding, which is adopted in the non-orthogonal multiple access technique. Thus it is very important to study the capacity region. Currently, the best inner bound is Marton’s inner bound, and the best outer bound is Nair-El Gamal outer bound. Noticing that we have shown the sub-optimality of this outer bound, in this proposal we will analyze the optimality of Marton’s inner bound. In particular, we study the following three key problems: The properties of the boundary points of Marton’s inner bound; Marton’s inner bound for Gaussian vector broadcast channels; Marton’s inner bound for general broadcast channels. If we show that this inner bound is optimal, we will continue to find practical encoding and decoding schemes to approach this inner bound, thus promote the advancement of technology; If it turns out that this inner bound is sub-optimal, we will try designing new encoding and decoding methods to get a better inner bound, thus develop theoretical results for the next generation communication.

广播信道是网络信息论的一个经典模型，模拟了单发送端多接收端通信场景的下行系统。该模型的一个核心问题是容量区域，其研究主要集中在该区域的内界和外界。早期的内界由叠加编码给出，该编码方法正被用于非正交多址接入技术的研究，因而研究该容量区域具有非常重要的意义。目前最好的内界是Marton内界，最好的外界是Nair-El Gamal外界。考虑到申请人及合作者已经证明了该外界不是最优的，本课题将分析Marton内界的最优性。我们将着重研究以下三个关键问题：Marton内界边界点的性质；高斯矢量广播信道的Marton内界；一般广播信道的Marton内界。如果证明该内界是最优的，接下来就可以研究实用的编解码方案以逼近该内界，进而促进科技进步；而如果证明该内界是次优的，我们可以寻求更好的编解码方案，得到更好的内界，帮助下一代移动通信建立更多的理论知识储备。

广播信道的容量区域分析是网络信息论的一个经典难题，其研究集中在该区域的内外界。项目组在本项目的资助下，一方面，从支撑超平面这一角度给出了若干外界的直接证明，为容量区域分析提供了一种崭新的思路；另一方面，利用扰动分析及线性矩阵不等式推进了高斯输入最优性的研究；最后，将相关成果结合深度学习做了交叉研究。在本项目支持下，项目组共发表SCI期刊论文2篇，顶级会议论文2篇，以及另外2篇国际会议论文；项目组一名硕士于2018年荣获上海市优秀毕业生称号。