Systems and control theory have found wide application in the analysis and design of numerical algorithms. We present an equivalent 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 SumProduct 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.
The BP algorithm has interesting structural properties corresponding to nonlinear feedback dynamical systems in the context of decoding the received signal REF .
Belief Propagation as a Dynamical System: The Linear Case and Open Problems
Iet Control Theory and Applications
Computer Science