  The performance and the decoding complexity of a novel coding scheme based on
the concatenation of maximum distance separable (MDS) codes and linear random
fountain codes are investigated. Differently from Raptor codes (which are based
on a serial concatenation of a high-rate outer block code and an inner
Luby-transform code), the proposed coding scheme can be seen as a parallel
concatenation of a MDS code and a linear random fountain code, both operating
on the same finite field. Upper and lower bounds on the decoding failure
probability under maximum-likelihood (ML) decoding are developed. It is shown
how, for example, the concatenation of a $(15,10)$ Reed-Solomon (RS) code and a
linear random fountain code over a finite field of order $16$, $\mathbb
{F}_{16}$, brings to a decoding failure probability $4$ orders of magnitude
lower than the one of a linear random fountain code for the same receiver
overhead in a channel with a erasure probability of $\epsilon=5\cdot10^{-2}$.
It is illustrated how the performance of the novel scheme approaches that of an
idealized fountain code for higher-order fields and moderate erasure
probabilities. An efficient decoding algorithm is developed for the case of a
(generalized) RS code.
