On hybrid factor graphs and adaptive equalization

Factor graphs may serve as a unifying framework for a wide variety of system models. Since the work of Wiberg (1996), there has been some awareness that factor graphs are also useful for tasks like equalization, channel estimation, synchronization, etc. In particular, factor graphs would allow the seamless integration of such sub-tasks into some “global” detection or estimation algorithm. A main issue in such applications is how to deal with continuous variables and with hybrid systems involving both discrete and continuous variables. These issues are addressed in the present paper, with a focus on equalization. It is shown that a variety of equalizing algorithms-some of them adaptive, all of them suitable for joint iterative decoding and equalization-fall right out of the general framework. Versions of most of these algorithms have previously been investigated by other authors using other notation, but some algorithms appear to be new