  Recent works showed how low-density parity-check (LDPC) erasure correcting
codes, under maximum likelihood (ML) decoding, are capable of tightly
approaching the performance of an ideal maximum-distance-separable code on the
binary erasure channel. Such result is achievable down to low error rates, even
for small and moderate block sizes, while keeping the decoding complexity low,
thanks to a class of decoding algorithms which exploits the sparseness of the
parity-check matrix to reduce the complexity of Gaussian elimination (GE). In
this paper the main concepts underlying ML decoding of LDPC codes are recalled.
A performance analysis among various LDPC code classes is then carried out,
including a comparison with fixed-rate Raptor codes. The results show that LDPC
and Raptor codes provide almost identical performance in terms of decoding
failure probability vs. overhead.
