Concise Derivation for Generalized Approximate Message Passing Using Expectation Propagation

Generalized approximate message passing (GAMP) is an efficient algorithm for the estimation of independent identically distributed random signals under generalized linear model. The sum-product GAMP has long been recognized as an approximate implementation of the sum-product loopy belief propagation. In this letter, we propose to view the message passing in a new perspective of expectation propagation (EP). Comparing with the previous methods that were based on Taylor expansions, the proposed EP method could unify the derivations for the real and the complex GAMP, with a difference only in the setup of Gaussian densities.