Patent ID: 8473824

Claim:
A method of generating parity information for user information in a low-density parity check (LDPC) encoder using a non-invertible parity check matrix H, the method comprising: calculating a quasi-cyclic LDPC generator matrix K based on the non-invertible parity-check matrix H and a quasi-cyclic square matrix M, wherein the quasi-cyclic square matrix M is selected from a plurality of predetermined matrices based on the non-invertible parity-check matrix H, and wherein the quasi-cyclic LDPC generator matrix K is calculated based on ΦK=M, where the non-invertible parity check matrix H is [ A B T C D E ] , F=(C+ET −1 A), and Φ=(D+ET −1 B), wherein A and C are circulants representing data portions of the non-invertible parity check matrix H, and wherein B, T, D, and E are circulants representing parity portions of the non-invertible parity check matrix H; storing the quasi-cyclic LDPC generator matrix K in a memory; and generating the parity information in the LDPC encoder based at least in part on the user information, the non-invertible parity check matrix H, and the quasi-cyclic LDPC generator matrix K.