Research On Construction And Encoding Algorithm Of Non-binary LDPC Codes

As the main candidate for forward error correction codes,Low Density Parity Check(LDPC)codes have been widely used in various communication systems.Compared with binary LDPC codes,non-binary LDPC codes have higher coding gain and are more suitable for high-order modulation,so it is more suitable for the development needs of largecapacity and high-speed optical communication systems.This paper focuses on the low-complexity encoding algorithm for non-binary LDPC codes,the high-gain construction method of spatially coupled(SC)LDPC codes,and the application performance of non-binary LDPC codes in spatial optical communication.1.The encoding complexity of the generation matrix encoding algorithm of the non-binary LDPC codes is proportional to the exponential power of the code length,and the complexity is too high.The encoding complexity of the RU(Richardson-Urbanke)encoding algorithm is reduced,but the algorithm changes the check relationship between the parity check matrix and the codeword,which affects the coding gain of the non-binary LDPC codes.In order to ensure no loss of coding gain,lowcomplexity encoding is realized at the same time,a non-binary LDPC code encoding algorithm based on rows and redundant columns permutation preprocessing is proposed,which can fully carry out the triangulation process of preprocessing without changing the original verification relationship.The simulation results show that the designed encoding algorithm makes the encoding complexity of the non-binary LDPC codes proportional to the code length,and 0.02～0.15dB of coding gain loss is avoided when the equivalent bit length of the codeword is 16000.2.Non-binary SC-LDPC codes can improve the coding gain,but the existing non-binary SC-LDPC code encoding ending methods will cause code rate loss and affect the decoding performance.In this paper,a replicate&mask non-binary SC-LDPC code encoding method with effective endings is proposed.This method uses the non-binary LDPC code as the underlying code,and applies the replicate&mask method to construct the binary base matrix.According to the code parameters,the range of the tail check sequence and matrix are determined,the constraint relationship is re-established,and the non-zero element random replacement criterion is used to ensure that the tail check matrix is full rank.Solve the tail check sequence according to the tail constraint relationship to avoid performance loss.The simulation results show that the designed encoding method can ensure that the code rate of the non-binary SC-LDPC code is not lost,and when the bit error ratio(BER)is on the order of 1E-6,it has a performance gain of 0.12dB compared with the non-binary SC-LDPC code constructed by the unwraping&progressive edge growth algorithm.3.The power loss in the channel and the burst error caused by atmospheric turbulence have a serious impact on the Free Space Optical(FSO)communication system,and the non-binary LDPC code has high gain and anti-burst error characteristics,so this paper studies and analyzes the application of the non-binary LDPC code in the FSO communication system,and proposes to apply the coding modulation scheme combining the non-binary LDPC code with high-order modulation to the FSO system.An 80Gbps non-binary LDPC coded modulation polarization multiplexing 16 quadrature amplitude modulation(NB-LDPC-CM-PM-16QAM)FSO coherent communication simulation system was established.The simulation analyzes the performance of the non-binary LDPC code under different turbulence intensities,different code rates,and different code lengths,and the simulation results verify the effectiveness of the NBLDPC-CM scheme in the FSO system.