CAREER: Coding for multiple-input multiple-output channels

本研究的目标是扩大我们的通信理论，信息理论和信号处理的知识，并在实际的无线通信系统和网络中产生直接的影响。本文的研究建立在空时编码的一般理论和码设计策略的基础上。 在这项研究中开发的数学方法，算法和概念是适用的，并在通信和应用数学的许多不同领域发起新的活动。这些领域包括调制解调器设计、均衡、波束形成、线性代数等。当然，直接的影响是提高无线通信系统的数据速率，以及推进我们对多输入多输出信道的行为的理解，目前，有一个基本的理论限制，禁止我们设计全速率正交空时分组码超过两个发射天线。 此外，现有的代码还没有达到信息论所声称的最佳性能，因此在可能的代码和今天的代码状态之间存在差距。我们试图通过设计新的代码类，提供充分的多样性，高速率，小的复杂性，高性能和数学上有趣的结构，以消除这一差距。

The goal of this research is to expand our knowledge of communication theory, information theory, and signal processing, and to make an immediate impact in practical wireless communication systems and networks. The research builds upon the general theory and code design strategy for space-time coding. The mathematical methods, algorithms, and concepts developed in this research is applicable and initiates new activities in many different areas of communications and applied mathematics. These areas include modem design, equalization, beam-forming, linear algebra, and soon. Of course, the immediate impacts are in increasing the data rates of wireless communication systems as well as advancing our understanding of the behavior of multiple-input multiple-outputchannels.Currently, there is a fundamental theoretical limit which prohibits us from designing full-rate orthogonal space-time block codes for more than two transmit antennas. Also, the available codes have not achieved the best performance claimed by information theory, so there exists a gap between what is possible, and the state of codes today. We seek to eliminate this gap by designing new classes of codes that provide full diversity, high rate, small complexity, high performance and mathematically interesting structures.