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

CIF:Small:RUI：MIMO 系统空时分组码的数学问题

• 批准号: 1318260
• 负责人: B Sethuraman
• 金额: $ 25万
• 依托单位: The University Corporation, Northridge
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-01 至 2018-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1318260&HistoricalAwards=false
• 关键词: CIF; Small; RUI; Mathematical; Problems

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.

研究人员研究了多输入多输出（MIMO）无线通信系统的编码和解码中出现的数学问题。这样的通信系统承诺更高的数据传输速率与更高的保真度比传统的单输入/输出系统，和PI研究的问题是直接相关的设计，这样的多输入/输出系统。本研究将集中于三大类问题：第一类是空时分组码的快速译码问题。人们可以通过将解码考虑直接纳入到代码的设计中来加速解码，或者也可以设计将利用代码的代数性质的近似解码方案。这两条路线都提出了具有挑战性的数学问题，研究人员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陪集码的设计。这个项目研究了在这种情况下出现的几个问题，包括确定所有可能的商环，适当的选择有限环上的代码，重要的是，适当的选择度量的代码上的商环。第三类问题涉及窃听信道的编码设计。在这里，研究人员研究了高斯信道的格猜想，然后继续考虑MIMO窃听信道的代码设计。