Several important relations between the cycle structure on the Tanner graph and the parity-check matrix H of LDPC codes were proved.A new algorithm for constructing LDPC codes was proposed that introduced quasi-cyclic ex-tension method to PEG algorithm.After a basic matrix was constructed with PEG algorithm

circulant permutation ma-trices would replace the "1"s in the basic matrix.The new method could eliminate effectively the short cycles in the basic matrix without changing the degree distribution fraction of the basic matrix.Simulations show that the quasi-cyclic extended codes based on PEG algorithm have as good error correcting performance as the LDPC codes generated by PEG algorithm in the same conditions of code length

rate

degree distribution and decoding algorithm.The conclusion of contrastive analysis is that well-chosen cycle structures can improve the decoding performance obviously under the given degree distribution.The proposed algorithm can offer a good performance and low encoding complexity synchronously by taking advantage of the quasi-cyclic code’s characteristic that its parity-check matrix H has less superposition within the cycles.