In this letter, we investigate quasi-cyclic low-density parity-check (QC-LDPC) codes in a 40-Gb/s nonreturn-to-zero differential phase-shift keying (NRZ-DPSK) signal transmission system based on a fiber-based optical parametric amplifier (FOPA). A constructed algorithm of QC-LDPC codes according to the optimizing set of shift values on the circulant permutation matrix (CPM) of the basis matrix is proposed. Simulation results prove that the coding gain in the encoded system can be realized at 10.2 dB under QC-LDPC codes with a code rate of 5/6 when the bit error rate (BER) is 10-9. In addition, the error-floor level originating from the uncoded system is suppressed.