LDPC Codes of Arbitrary Girth

For regular, degree two LDPC (low density parity-check) codes, there is a strong relationship between high girth and performance. This article presents a greedy algorithm, called successive level growth (SLG), for the construction of LDPC codes with arbitrarily specified girth. The simulation results show that our codes exhibit significant coding gains over randomly constructed LDPC codes and in some cases outperform PEG codes in the additive white Gaussian noise channel.