A novel construction method of quasi-cyclic low-density parity-check(QC-LDPC) code is proposed based on the finite field multiplicative group,which has easier construction,more flexible code-length code-rate adjustment and lower encoding/decoding complexity.Moreover,a regular QC-LDPC(5334,4962) code is constructed.The simulation results show that the constructed QC-LDPC(5334,4962) code can gain better error correction performance under the condition of the additive white Gaussian noise(AWGN) channel with iterative decoding sum-product algorithm(SPA).At the bit error rate(BER) of 10-6,the net coding gain(NCG) of the constructed QC-LDPC(5334,4962) code is 1.8 dB,0.9 dB and 0.2 dB more than that of the classic RS(255,239) code in ITU-T G.975,the LDPC(32640,30592) code in ITU-T G.975.1 and the SCG-LDPC(3969,3720) code constructed by the random method,respectively.So it is more suitable for optical communication systems.
A novel Reed Solomon （RS） block turbo code （BTC） coding scheme of RS（63,58）xRS（63,58） for optical communications is proposed. The simulation results show that the net coding gain （NCG） of this scheme at the sixth iteration is more than that of other coding schemes at the third iteration for the bit error rate （BER） of 10~2. Furthermore, the novel RS BTC has shorter component code and rapider encoding and decoding speed. Therefore, the novel RS BTC coding scheme can be better used in high-speed long-haul optical communication systems, and the novel RS BTC can be regarded as a candidate code of the super forward error correction （super-FEC） code~ Moreover, the encoding/decoding design and implementation of the novel RS BTC are also presented.
Based on the genetic algorithm(GA),a new genetic probability decoding(GPD) scheme for forward error correction(FEC) codes in optical transmission systems is proposed.The GPD scheme can further offset the quantification error of the hard decision by making use of the channel interference probability and statistics information to restore the maximal likelihood transmission code word.The theoretical performance analysis and the simulation result show that the proposed GPD scheme has the advantages of lower decoding complexity,faster decoding speed and better decoding correction-error performance.Therefore,the proposed GPD algorithm is a better practical decoding algorithm.
Based on the optimization and improvement for the construction method of systematically constructed Gallager (SCG) (4, k) code, a novel SCG low density parity check (SCG-LDPC)(3969, 3720) code to be suitable for optical transmission systems is constructed. The novel SCG-LDPC (6561,6240) code with code rate of 95.1% is constructed by increasing the length of SCG-LDPC (3969,3720) code, and in a way, the code rate of LDPC codes can better meet the high requirements of optical transmission systems. And then the novel concatenated code is constructed by concatenating SCG-LDPC(6561,6240) code and BCH(127,120) code with code rate of 94.5%. The simulation results and analyses show that the net coding gain (NCG) of BCH(127,120)+SCG-LDPC(6561,6240) concatenated code is respectively 2.28 dB and 0.48 dB more than those of the classic RS(255,239) code and SCG-LDPC(6561,6240) code at the bit error rate (BER) of 10 -7 .
An effective hierarchical reliable belief propagation(HRBP)decoding algorithm is proposed according to the structural characteristics of systematically constructed Gallager low-density parity-check(SCG-LDPC)codes.The novel decoding algorithm combines the layered iteration with the reliability judgment,and can greatly reduce the number of the variable nodes involved in the subsequent iteration process and accelerate the convergence rate.The result of simulation for SCG-LDPC(3969,3720)code shows that the novel HRBP decoding algorithm can greatly reduce the computing amount at the condition of ensuring the performance compared with the traditional belief propagation(BP)algorithm.The bit error rate(BER)of the HRBP algorithm is considerable at the threshold value of 15,but in the subsequent iteration process,the number of the variable nodes for the HRBP algorithm can be reduced by about 70%at the high signal-to-noise ratio(SNR)compared with the BP algorithm.When the threshold value is further increased,the HRBP algorithm will gradually degenerate into the layered-BP algorithm,but at the BER of 10-7and the maximal iteration number of 30,the net coding gain(NCG)of the HRBP algorithm is 0.2 dB more than that of the BP algorithm,and the average iteration times can be reduced by about 40%at the high SNR.Therefore,the novel HRBP decoding algorithm is more suitable for optical communication systems.
