  Decoding performance of Fountain codes for the binary erasure channel (BEC)
depends on two aspects. One is the essential code structure, on which stopping
set analysis operates. The other is the effect from the channel characteristic,
which is difficult to give a precise estimation. To tackle these problems, in
this paper, we propose a solution to analyzing the performance of Fountain
codes based on the uncorrectable set. We give the condition for Fountain
decoding failure over the BEC. Then, we conduct the analysis of uncorrectable
set on Fountain codes. Finally, we combine the stopping set and the
uncorrectable set to provide the integrated analysis on the performance of
Fountain codes for BEC.
