Methods and systems are disclosed herein for generating parity information for using information in a low-density parity check (LDPC) encoder. A quasi-cyclic LDPC generator matrix K can be generated based on the non-invertible parity-check matrix H. Parity information can be generated by 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.