  A scaling law developed by Amraoui et al. is a powerful technique to estimate
the block error probability of finite length low-density parity-check (LDPC)
codes. Solving a system of differential equations called covariance evolution
is a method to obtain the scaling parameter. However, the covariance evolution
has not been analytically solved. In this paper, we present the analytical
solution of the covariance evolution for irregular LDPC code ensembles.
