In order to increase the transmission distance of 100 Gbits/s optical communication systems

this paper constructs a high-gain Non-Binary Quasi-Cyclic Low-Density Parity Check（NB-QC-LDPC） code over the Galois Field GF（4）

which is suitable for 100 Gbit/s optical communication systems using QPSK or DQPSK modulation formats.Using the Logarithm Fourier Sum-Product Algorithm（Log-Fourier SPA）

it analyzes the BER performance of NB-QC-LDPC.The results show that compared with the binary QC-LDPC code

the NB-QC-LDPC code with a code length 500 and code rate 0.8 can provide approximately 1 dB coding gain at the BER of 10-8 and when the code rate decreases from 0.9 to 0.8 at the same BER

this code can provide additional code gain of about 0.6 dB

which means that the NB-QC-LDPC code outperforms the binary QC-LDPC code at the lower code rates.