Distance properties of irregular LDPC codes

In this paper, we investigate the distance properties of irregular LDPC codes using the ensemble construction proposed by Richardson et al (Ref. 2). By generalizing the method introduced by Gallager for regular LDPC codes [R.G. Gallager, 1963], we calculate the average weight distribution of irregular LDPC codes. Then, we interpret the stability condition of density evolution as a sufficient condition so that the error probability due to low weight codewords tends to zero under maximum-likelihood decoding.