Title: Division algebras: a tool for Space-Time Coding

                 Frederique Oggier
   Center for the Mathematics of Information
       California Institute of Technology

ABSTRACT: Division algebras are objects coming from the area of
non-commutative algebra. Traditionally studied as pure mathematical
objects, they have been recently shown to be a powerful tool for
designing codes for multiple antennas channels (also called Space-Time
codes).

In this second talk, I will present the so-called Golden code, which
is the best known code for the 2 antennas coherent MIMO channel, and
show how the fact that it has been designed from a cyclic division
algebra allows to prove its main property, the so-called non-vanishing
determinant property.  I will furthermore discuss other applications
of division algebras to coding problem, including the differential
non-coherent MIMO channel.