In this paper, we derive the average weight distributions for the irregular
non-binary cluster low-density parity-check (LDPC) code ensembles. Moreover, we
give the exponential growth rate of the average weight distribution in the
limit of large code length. We show that there exist (2,dcβ)-regular
non-binary cluster LDPC code ensembles whose normalized typical minimum
distances are strictly positive.Comment: 12pages, 6 figures, To be presented in ISIT2013, Submitted to IEICE
Trans. Fundamental