  We analyze the second moment of the ripple size during the LT decoding
process and prove that the standard deviation of the ripple size for an LT-code
with length $k$ is of the order of $\sqrt k.$ Together with a result by Karp
et. al stating that the expectation of the ripple size is of the order of $k$
[3], this gives bounds on the error probability of the LT decoder. We also give
an analytic expression for the variance of the ripple size up to terms of
constant order, and refine the expression in [3] for the expectation of the
ripple size up to terms of the order of $1/k$, thus providing a first step
towards an analytic finite-length analysis of LT decoding.
