Good encodable irregular quasi-cyclic LDPC codes

The existing encodable irregular LDPC codes may have a degraded BER performance when it is derived from classical regular QC LDPC codes since both girth property and weight property are not carefully given attention to two or more thing, which lead to some codes with large girths have small minimum weights and poor BER performance. To solve the problem, we propose a new approach to construct the encodable irregular QC codes, which can not produce new short girths and can keep the large minimum weight and minimum distance of the codes. The theorems of girth 4 and girth 6 are provided to test the girth variance of the obtained irregular QC codes. Simulations verify the construction of the QC LDPC codes to be valid, since better BER performance than that of existing encodable irregular LDPC codes is obtained.