  Raptor codes have been widely used in many multimedia broadcast/multicast
applications. However, our understanding of Raptor codes is still incomplete
due to the insufficient amount of theoretical work on the performance analysis
of Raptor codes, particularly under maximum-likelihood (ML) decoding, which
provides an optimal benchmark on the system performance for the other decoding
schemes to compare against. For the first time, this paper provides an upper
bound and a lower bound, on the packet error performance of Raptor codes under
ML decoding, which is measured by the probability that all source packets can
be successfully decoded by a receiver with a given number of successfully
received coded packets. Simulations are conducted to validate the accuracy of
the analysis. More specifically, Raptor codes with different degree
distribution and pre-coders, are evaluated using the derived bounds with high
accuracy.
