Average growth rate of low-density generator-matrix codes ensembles

We evaluate the average growth rate of the low-density generator-matrix (LDGM) code ensembles by applying the statistical-mechanical approach, which is called as the quenched average growth rate. In the existing analysis, the annealed average growth rate, which is the growth rate of the average weight distribution, has been evaluated. We explicitly show some examples of the difference between the annealed averaged and quenched averaged growth rate for the irregular sparse matrix ensemble.