5G Research in the Department of Mathematics and Systems Analysis
Processing data prior to transmission requires sophisticated mathematics, to be employed by the next-generation mobile industry standards to deliver data to growing networks quickly (algorithms must be low complexity) and for many users (schemes must be scalable). Roughly speaking, transmission over wireless channels is modelled by matrix equations over the complex numbers, wherein ‘encoding’ and ‘decoding’ matrices are to be engineered to increase data rate, eliminate interference, or speed up some algorithm.
Insisting, that a wireless communication system has some desirable property can often be boiled down to a ‘design criterion’ which forces an algebraic condition on the matrix (for example, that its column space is independent of some given subspace). Hence, aspects of wireless communications engineering can be viewed as applied algebra, where one constructs and optimizes over matrices satisfying natural algebraic conditions. Similar tools can be used to study distributed storage systems, which store files in a robust manner and have seen practical applications at large data centres at Facebook and Google. These algebraic tools have proven, and will continue to be invaluable, in communications engineering for the 5G standard.
The main research areas fall within coding theory, information theory and their various applications to Communications Engineering. More details at http://math.aalto.fi/en/research/algnumb/?SITE_LANG=en
Main contact person in the Department of Mathematics and Systems Analysis: Professor Camilla Hollanti