Distance spectrum of right-regular low-density parity-check codes: derivation and discussion of numerical results

The asymptotic distance distribution of regular low-density parity-check (LDPC) codes derived by Litsin and Sherlev (2002) is generalised for the case of irregular LDPC codes with constant check node degree. Numerical analysis of simple irregular LDPC codes with weight-two variable nodes shows that their minimum Hamming distance can be increased linearly with the code length when the maximum variable node degree of the code is kept below a critical value. This result is consistent with the stability condition of the LDPC codes, at least for the simple irregular case.