A duality theory for factor graphs

In this thesis, an extended theory of factor graphs is presented, which includes both the conventional multiplicative factor graphs and a new type of factor graph: convolutional factor graphs. A Fourier transform duality naturally exists between the two types of factor graphs. Both multiplicative and convolutional factor graphs can be used as probabilistic graphical models, on which efficient inference algorithms can be developed. The application of factor graph duality theory to codes on graphs is presented. The introduction of convolutional factor graphs leads to the discovery of a new fundamental property on probabilistic graphical models, namely, the Cox property on graphs. This in turn motivates a generalization of convolutional factor graphs. An application of generalized convolutional factor graphs in networking is presented.