Exact erasure channel density evolution for protograph-based generalized LDPC codes

We derive explicit density evolution equations for protograph-based generalized LDPC codes on the binary erasure channel. They are obtained from an analysis of multi-dimensional input/output transfer functions of the component decoders. Belief propagation decoding with optimal component APP decoders is considered. Based on the resulting transfer functions, a threshold analysis is performed for some protograph examples.