|Ph.D Student||Bustin Ronit|
|Subject||The Information-Estimation Approach for Multi-Terminal|
Problems in the Gaussian Regime
|Department||Department of Electrical Engineering||Supervisor||? 18? Shlomo Shamai )Shitz(|
|Full Thesis text|
We examine several multi-terminal information theory problems. The connecting thread among these problems is the approach used for their solution - usage of the connection between the mutual information and minimum mean square error (MMSE), referred to as the I-MMSE approach. This approach is based on a fundamental relationship between information theory and estimation theory in the Gaussian regime discovered by Guo et al.
The first problem investigated is the secrecy capacity of the MIMO Gaussian wiretap channel. The secrecy capacity was given as a non-convex optimization problem. Using the I-MMSE approach we were able to provide a closed form solution for this problem, including the optimal input covariance and the required enhancement.
Motivated by the scalar “single crossing point” property of Guo et al., which along with the I-MMSE relationship provided a simple and insightful converse proof to the capacity of the scalar Gaussian broadcast channel (BC), we extend this property to the parallel vector Gaussian channel. The extension is done in three phases and its applicability is demonstrated on information theoretic problems such as proving the parallel vector Gaussian BC capacity region under a per-antenna constraint, and a covariance constraint.
The third problem investigated is the properties of the minimum mean square error (MMSE) and mutual information of codes. Our purpose was to quantify the advantage of "bad" point-to-point codes in terms of MMSE. We show that the maximum possible rate of an MMSE constrained code is the rate of the corresponding optimal Gaussian superposition codebook. This result provides an engineering insight to the good performance of the Han-Kobayashi (HK) superposition scheme on the two-user interference channel.
Finally, we considered the Gaussian Z-interference channel and the type I Broadcast-Z-Interference Gaussian channel, both with weak interference. Using the I-MMSE relationship we were able to reproduce the best known outer bounds on the capacity region of these two multi-terminal settings. Our derivation is both simpler and provides insight to the reason why these bounds are not tight.
We conclude this dissertation with the presentation of several open problems and challenges which arise from the problems examined.