Neural Enhanced Belief Propagation on Factor Graphs

TL;DR

This paper introduces a hybrid model combining graph neural networks with belief propagation to improve inference accuracy in factor graphs, especially for error correction in LDPC codes over challenging channels.

Contribution

The work extends graph neural networks to factor graphs and proposes a hybrid model that enhances belief propagation with learned corrections, improving decoding performance.

Findings

Outperforms belief propagation in LDPC decoding on bursty channels

Combines GNNs with belief propagation for more accurate inference

Demonstrates effectiveness on error correction tasks

Abstract

A graphical model is a structured representation of locally dependent random variables. A traditional method to reason over these random variables is to perform inference using belief propagation. When provided with the true data generating process, belief propagation can infer the optimal posterior probability estimates in tree structured factor graphs. However, in many cases we may only have access to a poor approximation of the data generating process, or we may face loops in the factor graph, leading to suboptimal estimates. In this work we first extend graph neural networks to factor graphs (FG-GNN). We then propose a new hybrid model that runs conjointly a FG-GNN with belief propagation. The FG-GNN receives as input messages from belief propagation at every inference iteration and outputs a corrected version of them. As a result, we obtain a more accurate algorithm that combines the benefits of both belief propagation and graph neural networks. We apply our ideas to error correction decoding tasks, and we show that our algorithm can outperform belief propagation for LDPC codes on bursty channels.