Merging Belief Propagation and the Mean Field Approximation: A Free Energy Approach

TL;DR

This paper introduces a novel joint message passing algorithm that combines belief propagation and mean field approximation through a free energy framework, providing convergence guarantees and practical application to OFDM channel estimation.

Contribution

It develops a unified message passing approach based on free energy principles, enabling the integration of belief propagation and mean field methods with convergence assurances.

Findings

Fixed-point equations correspond to stationary points of a constrained free energy.

The method includes hard constraints in belief propagation.

Application demonstrated in OFDM channel estimation and decoding.

Abstract

We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al. We show that the message passing fixed-point equations obtained with this combination correspond to stationary points of a constrained region-based free energy approximation. Moreover, we present a convergent implementation of these message passing fixedpoint equations provided that the underlying factor graph fulfills certain technical conditions. In addition, we show how to include hard constraints in the part of the factor graph corresponding to belief propagation. Finally, we demonstrate an application of our method to iterative channel estimation and decoding in an orthogonal frequency division multiplexing (OFDM) system.