|Thesis abstract: |
Increasingly, in many engineering fields, a more appropriate characterization of the dynamical systems leads to a model where an accurate description of the underlying dynamics is obtained by including elements of non-linearity and non-Gaussianity. In the context of digital transmission systems the computation of posterior probabilities of the hidden Markov state of such systems is often required.
In these cases the exact Bayesian tracking of a posteriori probabilities of the state often becomes unfeasible and, therefore, resorting to approximated methods becomes necessary. In a continuous state scenario, a general way to realize approximated tracking is based on particle filtering methods that are sequential Monte Carlo approaches based on point mass representations of probability densities. Particle filtering, that can be seen as a generalization of the traditional Kalman filtering, can be applied to any continuous state-space model. In a discrete state application, the approximated tracking can be realized by adopting trellis-based algorithms, which often require the study of complexity reduction techniques. Starting from the definition of the state transition and observation models and without restrictive assumptions, these tracking methods have found widespread application in many research fields.
The thesis will focus on the computation of information rates in those communication channels where the a posteriori probabilities cannot be exactly tracked, such as phase noise channels, fading channels that can be modelled using a continuous state Gauss-Markov process, and channels with memory that can be found in molecular communication. Starting from the definition of mutual information, that is very difficult to compute for these channels, approximated Bayesian tracking methods can be used to calculate upper and lower bounds to the information rate. The goal of the work is to obtain upper and lower bounds as close as possible to each other, in order to compute an information rate close to actual one. The application of Bayesian tracking, as a mean to get the above bounds on the information rate, represents the main subject to be investigated in the major thesis.