Density Evolution for Expectation Propagation

Expectation propagation (EP) is a theoretical extension of the belief propagation family of message passing algorithms for statistical inference which allows for efficient handling of models with continuous random variables as well as second or higher order correlation via the use of standard exponential families of probability measures. Here we provide theoretically rigorous justifications for the use of density evolution to analyze the convergence and performance behavior of the family of algorithms in the large system regime by extending and expanding on the corresponding results for belief propagation decoding and turbo decoding.