Expectation Propagation is a generalization to Belief Propagation (BP) in twoways. First, it can be used with any exponential family distribution over thecliques in the graph. Second, it can impose additional constraints on themarginal distributions. We use this second property to impose pair-wisemarginal distribution constraints in some check nodes of the LDPC Tanner graph.These additional constraints allow decoding the received codeword when the BPdecoder gets stuck. In this paper, we first present the new decoding algorithm,whose complexity is identical to the BP decoder, and we then prove that it isable to decode codewords with a larger fraction of erasures, as the block sizetends to infinity. The proposed algorithm can be also understood as asimplification of the Maxwell decoder, but without its computationalcomplexity. We also illustrate that the new algorithm outperforms the BPdecoder for finite block-size
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