  In this paper we analyze LT and Raptor codes under inactivation decoding. A
first order analysis is introduced, which provides the expected number of
inactivations for an LT code, as a function of the output distribution, the
number of input symbols and the decoding overhead. The analysis is then
extended to the calculation of the distribution of the number of inactivations.
In both cases, random inactivation is assumed. The developed analytical tools
are then exploited to design LT and Raptor codes, enabling a tight control on
the decoding complexity vs. failure probability trade-off. The accuracy of the
approach is confirmed by numerical simulations.
