# A New Insight into GAMP and AMP

## TL;DR

This paper reveals a unified message passing framework that links expectation propagation, GAMP, and AMP, providing new insights into their relationships and potential for developing advanced algorithms for non-linear problems.

## Contribution

It derives a unified message passing rule connecting EP, GAMP, and AMP, offering a new perspective on their relationships and guiding future algorithm development.

## Key findings

- EP-MPA is equivalent to GAMP for general channels.
- EP-MPA reduces to AMP for Gaussian noise channels.
- Provides a unified view of message passing algorithms.

## Abstract

A concise expectation propagation (EP) based message passing algorithm (MPA) is derived for the general measurement channel. By neglecting some high-order infinitesimal terms, the EP-MPA is proven to be equivalent to the Generalized Approximate Message Passing (GAMP), which exploits central limit theorem and Taylor expansion to simplify the belief propagation process. Furthermore, for additive white gaussian noise measurement channels, EP-MPA is proven to be equivalent to the AMP. Such intrinsic equivalence between EP and GAMP/AMP offers a new insight into GAMP and AMP via a unified message passing rule for non-linear processing, and may provide clues towards building new MPAs in solving more general non-linear problems.