Weight distributions of multi-edge type LDPC codes

For a (lambda(x); rho(x)) standard irregular LDPC code ensemble, the growth rate of the average weight distribution for small relative weight omega is given by log(lambda´(0)rho´(1))omega + O(omega²) in the limit of code length n. If lambda´(0)rho´(1) < 1, there exist exponentially few code words of small linear weight, as n tends to infinity. It is known that the condition coincides with the stability condition of density evolution over the erasure channels with the erasure probability 1. In this paper, we show that this is also the case with multi-edge type LDPC (MET-LDPC) codes. MET-LDPC codes are generalized structured LDPC codes introduced by Richardson and Urbanke. The parameter corresponding lambda´(0)rho´(1) appearing in the conditions for MET-LDPC codes is given by the spectral radius of the matrix defined by extended degree distributions.