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.
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