Peter Oswald

Some approximation problems arising in communications

At the danger of being laughed at for lack of professionalism, I will share some examples of approximation problems that I encountered, mostly through consulting other researchers in Bell Laboratories' basic research unit, during my last 6 years with Lucent Technologies. Most of them are outside my immediate area of expertise but seemed important enough to learn about and work on for a while. The examples I will talk about in more detail will be:
1) Fast encoding-decoding of low-density parity check codes (properties of power series, polynomial inequalities,...)
2) Polarization mode dispersion in optical transmission systems (SU(2)- resp. SO(3)-valued functions) and, time permitting,
3) Optimal design of multiple-antenna codes ("equi-distant" distribution of matrices and nonlinear approximation).
After a brief motivational introduction to each subject, I will try to characterize the approximation-theoretic part of its mathematical formulation, and give a summary of results (if there were any) and open problems.