CIF: Small: Collaborative Research: Wireless Networks: Fundamental Limits via Extremal Entropy Properties

CIF：Small：协作研究：无线网络：通过极值熵特性确定基本极限使用极值熵特性来表征网络通信的基本性能极限是信息论的传统。然而，大多数历史上的成功都依赖于一个特殊的极值熵不等式：Shannon和Stam的熵-幂不等式，尽管它很强大，但主要适用于具有一定退化结构的网络。此外，多输入多输出(MIMO)通信等无线特性、衰落引起的信道不确定性以及无线电通信的广播性导致的保密性限制带来了新的挑战，而仅靠Shannon和Stam的熵-功率不等无法克服这些挑战。这就需要深入研究网络信息论中的逆问题和统计学中的极值熵性质之间的相互作用，借助于强大的统计工具来解决重要的通信工程问题。本研究的具体目标是：1)考察通过信息论和统计学之间的联系来建立极值熵性质的系统方法；2)建立信道增强作为解决MIMO下行链路通信逆问题的通用框架；3)确定认知无线网络中协作通信逆问题的一般解决框架。近年来，人们在设计新的编码方案以实现更好的无线网络性能方面付出了大量的努力。因此，从工程的角度来看，从根本上了解这些编码方案的局限性对于指导未来的研究、防止过度设计以及增强对简单和结构化编码方案的信心是极其重要的。从这项研究中获得的智力成果也将通过德克萨斯农工大学和夏威夷大学关于网络信息理论和无线通信的课程发展来传播。

CIF: Small: Collaborative Research: Wireless Networks: Fundamental Limits via Extremal Entropy PropertiesUsing extremal entropy properties to characterize the fundamental performance limits of network communication is a tradition of information theory. Most historical successes, however, relied on one particular extremal entropy inequality: the entropy-power inequality of Shannon and Stam, which, though powerful, applies mainly to networks with certain degradedness structure. Moreover, wireless features such as multiple-input multiple-output (MIMO) communications, channel uncertainty incurred by fading, and secrecy constraints due to the broadcast nature of radio communication bring new challenges that cannot be overcome by the entropy-power inequality of Shannon and Stam alone. This situation calls for in-depth investigations of the interaction between converse problems in network information theory and extremal entropy properties in statistics, resorting to powerful statistical tools to solve important communication engineering problems.The specific goals of this research are: 1) to examine systematic ways of establishing extremal entropy properties through links between information theory and statistics; 2) to establish channel-enhancement as a general framework for solving the converse problems for MIMO downlink communication; and 3) to identify general frameworks for solving the converse problems for collaborative communication in cognitive wireless networks. Recent years have seen substantial efforts in designing new coding schemes to achieve better performance for wireless networks. Fundamental understanding of the limits of these coding schemes is thus extremely important from the engineering viewpoint to direct future research and to prevent over-engineering and bolster confidence for simple and structured coding schemes. Intellectual results obtained from this research will also be disseminated via course developments on network information theory and wireless communications at Texas A&M and the University of Hawaii.