We present a discrete-time dynamical system interpretation of an
algorithm commonly used in information theory called Belief
Propagation. Belief Propagation (BP) is one instance of the so-called
Sum-Product Algorithm and arises, e.g., in the context of iterative
decoding of Low-Density Parity-Check codes. We review a few known
results from information theory in the language of dynamical systems
and show that the typically very high dimensional, nonlinear dynamical
system corresponding to BP has interesting structural properties. For
the linear case we completely characterize the behavior of this
dynamical system in terms of its asymptotic input-output map.
Finally, we state some of the open problems concerning BP in terms of
the dynamical system presented.