A Note on Analytical Solution of Covariance Evolution for Regular LDPC Codes

摘要

The covariance evolution is a system of differential equations which gives the covariance of each random variable corresponding to the number of edges connecting to the nodes of each residual degree. Solving the covariance evolution, then we can derive the distribution 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 intensive numerical computations to solve the covariance evolution. In this report, we consider an analytical solution of the covariance evolution.