Factor Graphs in Wirless Communications: Theory and Practice by Henk Wymeersch
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In this two-part tutorial, we will cover the theory behind Bayesian graphical models as well as some practical applications. A background in probability theory and digital communications is recommended.
In Part I, we start with the three basic problems in Bayesian inference and highlight the computational issues that arise in high dimensions. We then introduce factor graphs as a way to represent high-dimensional distributions. On these factor graphs, we can execute a variety of message passing algorithms, such as sum-product, max-sum, and mean-field. We will connect each of these message passing algorithms with the basic problems in Bayesian inference. By means of a variational interpretation, we demonstrate how message passing algorithms can be interpreted, and how new message passing algorithms may be developed. We conclude with a discussion regarding convergence and distributed processing. In Part II, we will apply factor graphs to three practical problems: (i) receiver design (including equalization, demodulation, and decoding); (ii) synchronization; (iii) cooperative processing in networks. This part of the tutorial will contain do-it-yourself problems to get hands-on experience. Time permitting, we will give an overview of where factor graphs are currently being applied on the field of communication theory.