# Discrete signaling over general channel

Elektrotechnik Diplomarbeiten (Mai 2009 - Oktober 2009)## Betreuer

Anke Schmeink,## Abstract

The classical result from Shannon shows that the scalar additive Gaussian noise channel subject to average power constraints achieves capacity if the input distribution is Gaussian as well. However, due to its unbounded support this distribution is not realizable in practice. Further research has focused on bounded signaling sets by introducing peak power constraints of different types. The capacity-achieving distribution then becomes discrete with finite support. From a practical point of view, the signaling points should be kept discrete and bounded. The condition of capacity-achieving input distribution over a finite support of signaling points was proved by some previous works. Furthermore, this optimum distribution could be found using some iterative algorithms though with high computational complexity. With these knowledge, we think about the following questions: How to compute the optimum input distribution more efficiently? Given a finite set of signaling points, how to find a reduced subset and the corresponding distribution, which may provide near capacity performance as the original support and reduce significantly the complexity of receiver design? How does the constellation of this subset look like? The task of this thesis is to design efficient algorithms to solve these problems.