EXIT and Density Evolution Analysis for Homogeneous Expectation Propagation

We extend Gaussian approximation density evolution (DE) techniques from the soft iterative decoding of turbo and low density parity check (LDPC) codes to the performance and convergence analysis of belief propagation (BP) and expectation propagation (EP) in randomly connected very large sparse homogeneous factor graphs. A strict form of the Gaussian approximation allows the use of extrinsic information transfer (EXIT) charts to study the performance and convergence of the algorithms. The result is a graphical tool that design engineers can use to quickly predict the performance and convergence speed of BP or EP applied to these inference problems. We demonstrate the utility of the new tool, and a motivation for the generalization of the results, by showing how it may surprisingly be applied to determine the performance of a scheme for distributed data fusion in a sensor network.