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This is possible down to low error rates and even for small and moderate block sizes. The decoding complexity of ML decoding is kept low thanks to a class of decoding algorithms, which exploit the sparseness of the parity\u2010check matrix to reduce the complexity of Gaussian elimination. ML decoding of LDPC codes is reviewed at first. A performance comparison among various classes of LDPC codes is then carried out, including a comparison with fixed\u2010rate Raptor codes for the same parameters. The results confirm that a judicious LDPC code design allows achieving a near\u2010optimum performance over the erasure channel, with very low error floors. Furthermore, it is shown that LDPC and Raptor codes, under ML decoding, provide almost identical performance in terms of decoding failure probability vs. overhead. 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