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

Erwin Riegler, Gunvor Elisabeth Kirkelund, Carles Navarro Manchón, Mihai-Alin Badiu, Bernard Henri Fleury

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78 Citations (Scopus)
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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 fixed-point 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 OFDM system.
Original languageEnglish
JournalI E E E Transactions on Information Theory
Volume59
Issue number1
Pages (from-to)588-602
Number of pages15
ISSN0018-9448
DOIs
Publication statusPublished - Jan 2013

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