The estimation of the average distance distribution in ensembles of irregular low-density parity-check (LDPC) codes was discussed using asymptotic expressions. The derivation defined the considered ensemble of irregular codes and the average distance distribution. The number of matrices belonging to the ensemble of special shape were counted. The defined codes contained the word with on the first ω positions and zero on the remaining positions. A discussion on the number of solutions to a system of equation appearing in the optimization problem was also presented.
- Distance distributions
- Low-density parity-check (LDPC) codes