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A lower bound on the maximum likelihood (ML) decoding error exponent oflinear block code ensembles, on the erasure channel, is developed. The lowerbound turns to be positive, over an ensemble specific interval of erasureprobabilities, when the ensemble weight spectral shape function tends to anegative value as the fractional codeword weight tends to zero. For theseensembles we can therefore lower bound the block-wise ML decoding threshold.Two examples are presented, namely, linear random parity-check codes andfixed-rate Raptor codes with linear random precoders. While for the former afull analytical solution is possible, for the latter we can lower bound the MLdecoding threshold on the erasure channel by simply solving a 2 x 2 system ofnonlinear equations.

A Lower Bound on the Error Exponent of Linear Block Codes over the Erasure Channel