Iterative decoding of compound codes by probability propagation in graphical models

We present a unified graphical model framework for describing compound codes and deriving iterative decoding algorithms, After reviewing a variety of graphical models (Markov random fields, Tanner graphs, and Bayesian networks), we derive a general distributed marginalization algorithm far functions described by factor graphs. From this general algorithm, Pearl's belief propagation algorithm is easily derived as a special case, We point out that recently developed iterative decoding algorithms for various codes, including "turbo decoding" of parallel-concatenated convolutional codes, may be viewed as probability propagation in a graphical model of the code, We focus on Bayesian network descriptions of codes, which give a natural input/state/output/channel description of a code and channel, and we indicate how iterative decoders can be developed for parallel- and serially concatenated coding systems, product codes, and low-density parity-check codes.