An introduction to factor graphs

Graphical models such as factor graphs allow a unified approach to a number of key topics in coding and signal processing such as the iterative decoding of turbo codes, LDPC codes and similar codes, joint decoding, equalization, parameter estimation, hidden-Markov models, Kalman filtering, and recursive least squares. Graphical models can represent complex real-world systems, and such representations help to derive practical detection/estimation algorithms in a wide area of applications. Most known signal processing techniques -including gradient methods, Kalman filtering, and particle methods -can be used as components of such algorithms. Other than most of the previous literature, we have used Forney-style factor graphs, which support hierarchical modeling and are compatible with standard block diagrams.