  The covariance evolution is a system of differential equations with respect
to the covariance of the number of edges connecting to the nodes of each
residual degree. Solving the covariance evolution, we can derive distributions
of the number of check nodes of residual degree 1, which helps us to estimate
the block error probability for finite-length LDPC code. Amraoui et al.\
resorted to numerical computations to solve the covariance evolution. In this
paper, we give the analytical solution of the covariance evolution.
