DIMACS Theoretical Computer Science Seminar

Title: Algebraic Constructions of Grassmannian Packings

Speaker: Alexei Ashikhmin, Bell Labs

Date: Wednesday, November 28, 2007 11:00-12:00pm

Location: CoRE Bldg, CORE A, Room 301, Rutgers University, Busch Campus, Piscataway, NJ


A Grassmannian packing is a collection of subspaces in the embedding complex space. A good packing has to have large size and large minimum distance, that is any two subspaces of the packing have to be far away from each other in some since. Grassmannian packings find applications in statistics and wireless communications.

In this talk we present two algebraic constructions of Grassmannian packings. The first construction is based on the use of the extras-pecial group and a generalization of Boolean functions for the case of linear operators. The second construction is based on a generalization of some results of representation theory. The obtained Grassmannian packings are strongly related to standard binary Reed-Muller codes; in particular, they can be decoded by adapting a decoding algorithm for Reed-Muller codes.

In the second part of the talk I outline the application of the Grassmannian packings to information transmission through MIMO noncoherent channel.

Talk is based on joint works with A. R. Calderbank.