  Raptor code ensembles with linear random outer codes in a fixed-rate setting
are considered. An expression for the average distance spectrum is derived and
this expression is used to obtain the asymptotic exponent of the weight
distribution. The asymptotic growth rate analysis is then exploited to develop
a necessary and sufficient condition under which the fixed-rate Raptor code
ensemble exhibits a strictly positive typical minimum distance. The condition
involves the rate of the outer code, the rate of the inner fixed-rate Luby
Transform (LT) code and the LT code degree distribution. Additionally, it is
shown that for ensembles fulfilling this condition, the minimum distance of a
code randomly drawn from the ensemble has a linear growth with the block
length. The analytical results can be used to make accurate predictions of the
performance of finite length Raptor codes. These results are particularly
useful for fixed-rate Raptor codes under maximum likelihood erasure decoding,
whose performance is driven by their weight distribution.
