We consider the estimation of correlated Gaussian samples in (correlated) impulsive noise, through message-passing algorithms. The factor graph includes cycles and, due to the mixture of Gaussian (samples and noise) and Bernoulli variables (the impulsive noise switches), the complexity of messages increases exponentially. We first analyze a simple but suboptimal solution, called Parallel Iterative Scheduling. Then we implement both Expectation Propagation — for which numerical stability must be addressed — and a simple variation thereof (called Transparent Propagation) that is inherently stable and simplifies the overall computation. Both algorithms reach a performance close to ideal, practically coinciding with the lower bound on the mean square estimation error.
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