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.
