Seminars

Algebraic number theory has proved to be a useful tool in
the design of lattices suitable for multiantenna communication. Cyclic
division algebras over a numbeer field proved to be very useful in the
case of point-to-point communication (aka single user MIMO). More
recently constructions depending on algebraic number fields have also
been proposed for multiple access applications, where two or more
users use the same radio resource simultaneously. In the single user
case there is a well understood notion of the trade-off between the
available
code rate and its diversity (=a figure of merit describing the
reliability of the communication system). We shall review the concepts
and results of that theory, and the role played by constructions based
on algebraic numbers. In the multi-user case similar trade-off results
have been presented, but the theory is less clear. Some of the results
depend on the properties of the rate of decay of the determinants of
the code matrices. In this talk
I will discuss some preliminary general results, and thoroughly
dissect a simple promising code. Diverse simple techniques such as the
pigeon hole principle, Diophantine approximation, and elementary
Galois theory prove to be useful.