Research On The Construction Method Of NB-LDPC Codes

As a strong candidate code for the third-generation forward error correction,binary low density parity check(B-LDPC)code has been extensively used in high-speed optical communications due to its low-complexity codec structure and excellent error correction performance.The nonbinary LDPC(NB-LDPC)code has the superiority of higher net coding gain,better burst correcting ability,and suitable for high-order modulation communication systems by comparison with the B-LDPC code when the code length is short or medium.This paper mainly focuses on three research points:the construction method of NB-LDPC codes under certain degree distribution,the column weight distribution of irregular NB-LDPC codes,and the soft information calculate method of LDPC encode combined with pulse position modulation(PPM)system which has low complexity.The main contents of this research work are listed as follows.1.In view of the fact that the existing structured construction method still has a certain performance loss compared with the random construction method,in order to improve the coding gain of the NB-LDPC code,this paper proposes a construction method of NB-LDPC code based on local optimal searching(LOS)algorithm combined with optimal tuple and full rank condition(FRC)replacement.The proposed construction method uses the block progressive search LOS algorithm in the construction of the binary mother matrix.The selection of non-zero elements adopt the optimal tuple and FRC substitution criteria.Under Binary Phase Shift Keying(BPSK)modulation and Additive White Gaussian Noise(AWGN)channel conditions,the simulation results show that the proposed method based on the LOS algorithm combined with the optimal tuple and FRC replacement constructs a nonbinary quasi-cyclic LDPC(NB-QC-LDPC)with a larger girth or a smaller number of short circles under a certain degree of distribution.When the bit error rate(BER)is 10-7,the NB-QC-LDPC code constructed by the proposed method compared with the NB-QC-LDPC code constructed by progressive edge growth quasi-cyclic(PEG-QC)method combined with random non-zero element replacement can achieve 0.5dB performance improvement.2.As one of the important factors affecting the performance of the waterfall zone of irregular LDPC codes,the column weight distribution is of great significance for constructing NB-LDPC codes with higher coding gain.Although the theories of density evolution,gaussian elimination,and EXIT chart of B-LDPC codes have been extended to NB-LDPC codes.Due to the high complexity and it is only the result of the threshold analysis,so it is rarely used in actual code design.In this paper,based on the code words constructed in practice,the column weight distribution of NB-LDPC have been analyzed by monte carlo simulation and carries out the optimal column weight distribution of NB-QC-LDPC codes.In addition,this paper compares the performance of each order of NB-LDPC codes under the optimal column weight distribution condition.Under BPSK modulation and AWGN channel conditions,the simulation proves that the performance of the high-order NB-QC-LDPC code under the optimal column weight distribution is better.At BER=10-6,the NB-QC-LDPC code with the equivalent bit length of 3600 in the GF(64)domain with a code rate of 0.8 compared with the B-QC-LDPC code with a column weight of 3 which is commonly used can achieve about 0.3dB performance gain.3.LDPC coding combined with PPM modulation technology is a common coding modulation technology in space optical communication and underwater optical communication systems.However,it is urgent to reduce the implementation complexity of soft information calculation at the receiver.Based on the background that the theoretical soft information calculation method has exponential and logarithmic operations that are not friendly to hardware implementation and the performance loss of existing optimization schemes is large,this paper proposes a Max-Max low-complexity LDPC coding joint PPM modulation system soft information calculation method through mathematical approximation.Through the analysis of the complexity of each method and the comparison of simulations,it is proved that the proposed method can effectively reduce the complexity by 83.3%.The performance loss of the proposed method using log-domain belif propagation decoding algorithm in the 4PPM and AWGN channel is only 0.05dB compared with the theoretical method when BER=10-5,and the performance improvement compared with power ratio method is 0.5dB when BER=10-5 in weakly turbulent channel.