CIF:Small:RUI: Mathematical Problems in Space-Time Block Codes for MIMO Systems

研究者研究了多输入多输出（MIMO）无线通信系统编码和解码中出现的数学问题。与传统的单输入/输出系统相比，这种通信系统保证了更高的数据传输速率和更高的保真度，PI研究的问题与这种多输入/输出系统的设计直接相关。本研究将重点关注三大类问题。第一类讨论了空时分组码的快速解码问题。可以通过将解码考虑因素直接纳入代码设计来加快解码速度，或者也可以设计利用代码代数特性的近似解码方案。这两条路线都抛出了具有挑战性的数学问题，研究者研究了这些问题的各种解决方案。第二类问题涉及慢衰落信道的协集码的设计。本课题研究了在此背景下出现的几个问题，包括所有可能商的确定，有限环上码的适当选择，以及重要的是，商环上码上度量的适当选择。第三类问题涉及窃听信道的编码设计。在这里，研究者研究了高斯信道的晶格猜想，然后继续考虑MIMO窃听信道的编码设计。

The investigator studies mathematical problems that arise in coding and decoding for multiple-input-multiple-out (MIMO) wireless communications systems. Such communication systems promise much higher rates of data transfer with much higher fidelity than traditional single input/output systems, and the problems that the PI studies are of direct relevance to the design of such multiple input/output systems. There are three broad classes of problems the research will focus on. The first class deals with issues in fast decoding of space-time block codes. One can speed up decoding by incorporating decoding considerations directly into the design of the code, or, one can also design approximate decoding schemes that will take advantage of the algebraic nature of the codes. Both routes throw up challenging mathematical issues, and the investigator studies various solutions to these. The second class of problems deals with the design of coset codes for slow fading channels. This project studies several problems that arise in this context, including determination of all possible quotients, appropriate choice of codes over finite rings, and importantly, appropriate choice of metric on the code over the quotient ring. The third class of problems deals with the design of codes for the wiretap channel. Here, the investigator studies a lattice conjecture for the Gaussian channel, then moves on to consider the design of codes for the MIMO wiretap channel.