Information Theoretical Studies of Non-Gaussian Noise Channels and Markovian Constrained Relay Channels

Communications in non-Gaussian noise channel and communication network with memory are two important but difficult frontiers of information theory. In this thesis, I studied these two areas. In the first part of this thesis, the Gaussian mixture distribution is adopted to model the non-Gaussian noise behaviour, typically found in powerline communications, man-made electromagnetic interferences, and underwater communications. Here, the capacity of a Gaussian mixture noise channel and its capacity-achieving input distribution are investigated. In the second part, I studied the capacity of a Markovian constrained relay channel and the maxentropic state transition probabilities for relay transmitter are derived. The derived results have been verified via a number of simulations.