A novel QC-LDPC code based on the finite field multiplicative group for optical communications

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.

Construction of a new regular LDPC code for optical transmission systems

A novel construction method of the check matrix for the regular low density parity check （LDPC） code is proposed. The novel regular systematically constructed Gallager （SCG）-LDPC（3969,3720） code with the code rate of 93.7% and the redundancy of 6.69% is constructed. The simulation results show that the net coding gain （NCG） and the distance from the Shannon limit of the novel SCG-LDPC（3969,3720） code can respectively be improved by about 1.93 dB and 0.98 dB at the bit error rate （BER） of 10s, compared with those of the classic RS（255,239） code in ITU-T G.975 recommendation and the LDPC（32640,30592） code in ITU-T G.975.1 recommendation with the same code rate of 93.7% and the same redundancy of 6.69%. Therefore, the proposed novel regular SCG-LDPC（3969,3720） code has excellent performance, and is more suitable for high-speed long-haul optical transmission systems.

A novel decoding algorithm based on the hierarchical reliable strategy for SCG-LDPC codes in optical communications

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.

Comparative analysis on the performance of two concatenated codes for high-speed long-haul optical communication systems

After the development trend of high-speed long-haul optical communication systems and the theory of the concatenated code are analyzed,the comparative researches on the performances of the two concatenated codes of the inner-outer type and the improved interleaving type are performed in detail.The theoretical analyses and simulation results show that the inner-outer type concatenated code has the greater redundancy,and the improved interleaving type concatenated code is a superior concatenated code with the advantages of the better error correction performance,moderate redundancy and easy implementation.As a result,the improved interleaving type concatenated code can be better used in high-speed long-haul optical communication systems.

A novel concatenated code based on the improved SCG- LDPC code for optical transmission systems

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 .

A novel BTC decoding algorithm based on the genetic algorithm in optical communication systems

Combining the advantages of both the genetic algorithm(GA) and the chase decoding algorithm, a novel improved decoding algorithm of the block turbo code(BTC) with lower computation complexity and more rapid decoding speed is proposed in order to meet the developing demands of optical communication systems. Compared with the traditional chase decoding algorithm, the computation complexity can be reduced and the decoding speed can be accelerated by applying the novel algorithm. The simulation results show that the net coding gain(NCG) of the novel BTC decoding algorithm is 1.1 dB more than that of the traditional chase decoding algorithm at the bit error rate(BER) of 10-6. Therefore, the novel decoding algorithm has better decoding correction-error performance and is suitable for the BTC in optical communication systems.

A new probability decoding scheme based on genetic algorithm for FEC codes in optical transmission systems

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.

An improved noise reduction transformation for algorithm based on wavelet MEMS gyroscope

To solve the large noise problem for the low- precision gyroscopes in micro-electro mechanical systems （MEMS） of inertial navigation system, an improved noise reduction method, based on the analyses of the fast Fourier transformation （FFT） noise reduction principle and the simple wavelet noise reduction principle, was proposed. Furthermore, the FFT noise reduction method, the simple wavelet noise reduction method and the improved noise reduction method were comparatively analyzed and experimentally verified in the case of the constant rate and dynamic rate. The experimental analysis results showed that the improved noise reduction method had a very good result in the noise reduction of the gyroscope data at different fi：equencies, and its performance was superior to those of the FFT noise reduction method and the simple wavelet noise reduction method.