CIF:Medium:Collaborative Research: Geometric Network Information Theory

通信网络的扩散意味着它们的效率和安全性现在几乎影响到我们日常生活的方方面面。在社会层面，可靠和高效的网络对技术发展、国民经济增长和国防至关重要。鉴于此，了解网络设备的基本信息限制的问题比以往任何时候都更加尖锐。不幸的是，在信息论中，系统地将其成功扩展到经典的点对点信息交换之外一直是一个长期的挑战。尽管自1948年该领域成立以来进行了大量的研究，但大多数网络设置的信息限制，即使是像三节点中继通道这样基本的网络，到目前为止仍然是开放的。这个项目旨在改变当今信息论中分析许多网络问题的方式。用于量化网络基本性能限制的传统信息理论方法经常失败，因为当前的信息理论工具集没有足够的改进来描述由于竞争目标而出现的网络紧张关系。超越传统方法，该项目将研究几何和功能分析中的不等式在描述信息度量之间的紧张关系方面所起的作用。该研究项目将与一个强大的校际教育计划相辅相成，其中包括联合和合作的学生和博士后研究人员建议。

The proliferation of communication networks means that their efficiency and security now affects almost all aspects of our daily lives. At the societal level, reliable and efficient networks are of central importance to technological development, national economic growth and national defense. In light of this, the problem of understanding fundamental information limits of networked devices is more acute now than ever. Unfortunately, it has been a longstanding challenge in information theory to systematically extend its success beyond classical point-to-point exchanges of information. Despite significant research effort since the inception of the field in 1948, the information limits for most network settings, even for networks as fundamental as a three node relay channel, have remained open to date.This project aims to change the way many network problems are analyzed today in information theory. Traditional information-theoretic approaches for quantifying fundamental performance limits of networks often fail because the current toolset of information theory is not sufficiently refined to characterize tensions that emerge in networks due to competing objectives. Looking beyond traditional methods, this project will study the role that inequalities from geometric and functional analysis can play in characterizing tensions between information measures. The research project will be complemented with a strong inter-university education program, which includes joint and collaborative student and post-doctoral researcher advising.