  Expectation Propagation is a generalization to Belief Propagation (BP) in two
ways. First, it can be used with any exponential family distribution over the
cliques in the graph. Second, it can impose additional constraints on the
marginal distributions. We use this second property to impose pair-wise
marginal distribution constraints in some check nodes of the LDPC Tanner graph.
These additional constraints allow decoding the received codeword when the BP
decoder 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 is
able to decode codewords with a larger fraction of erasures, as the block size
tends to infinity. The proposed algorithm can be also understood as a
simplification of the Maxwell decoder, but without its computational
complexity. We also illustrate that the new algorithm outperforms the BP
decoder for finite block-size
