Research On The Techniques Of QC-LDPC Based Coded Modulation For Coherent Optical Communication Systems

The higher-order modulation format is one of the key technologies to achieve the large capacity transmission for coherent optical communication systems.However,with the increase of the modulation order,the bit-error rate(BER)of systems will drop dramatically since the less tolerance to the amplified spontaneous emission(ASE)noise and other signal impairments.Therefore,the reliable transmission over long distance can not be guaranteed easily.Coded modulation(CM),that refers to the combination of soft decision forward error correction(FEC)codes and higher-order modulation formats,can achieve higher spectral efficiency and power efficiency transmission while keeping the reliable transmission with target BER requirement.As one of the strong candidates of the third generation FEC coding scheme,quasi-cyclic low-density parity-check(QC-LDPC)codes not only have the BER performance approaching the Shannon limit,but also have good structural characteristics which facilitates the hardware implementation of their encoders and decoders.Therefore,QC-LDPC code based CM technology possesses significant research value.To further bridge the gap between the BER performance and the theoretical limit of the coherent optical communication system,there are still some key problems should be solved.For example:The design and construction of binary QC-LDPC(B-QC-LDPC)codes with low error-floor and high net coding gain(NCG);The channel capacity-approaching irregular B-QC-LDPC code based multi-level coded modulation(MLCM)scheme;The channel capacity-approaching non-binary QC-LDPC(NB-QC-LDPC)code based CM scheme with low complexity and et al.In this paper,the research mainly focus on the above metioned key problems.The main work and innovative contributions are listed as follows.1.Aiming at the problem of the performance degradation of the sum-product decoding algorithm(SPA)caused by the short cycles in the Tanner graph of the LDPC code,a sub-array cycle detection,pre-masking and local optimal searching based QC-LDPC code construction method is proposed to further reduce the number of the shorest cycles and/or enlarge the girth of the Tanner graph of B-QC-LDPC code with given degree distribution.Firstly,by detecting the non-repeated automatic enumerative cycles in the frame of sub-arrays,cycle detection time can be greatly reduced;Secondly,the introduction of pre-masking can eliminate all the constraints in addition to the degree distribution when designing the masking matrix,and the pre-masked exponential base matrix contains lots of zero matrices(ZMs),thus the pre-masking technique can make the design of masking matrix very simple and reduce the number of circulant permutation matrices(CPMs)that needed to be local optimized;Finally,the proposed local optimal searching technique could transform the global random optimal searching into the progressive local optimal searching that makes the searching more efficient.Therefore,the proposed construction method could construt B-QC-LDPC codes with less number of shortest cycles and/or larger girth.Simulation results show that,at the BER of 10-9,B-QC-LDPC codes construced by the proposed construction method can achieved 0.1dB?0.3dB performance improments compared with the B-QC-LDPC codes construced by the referenced methods when decoded with SPA under the BPSK AWGN channel.2.Irregular LDPC codes have the excellent BER performance in waterfall region,but usually show the error-floor phenomenon early that makes them unable to meet the BER requirement of the coherent optical communication systems.The stopping sets and low-weight codeword are the two main factors that causes the error-floor of LDPC codes,but their measurement is a NP-hard problem.To obtain the irregular B-QC-LDPC codes with the optimized stopping sets and low-weight codeword,or to say with low error-floor and high NCG in error-floor region,we consider the design and construction of irregular B-QC-LDPC codes by jointly optimizing the degree distribution,girth,the number of short cycles and approximate cycle extrinsic information degree(ACE),each of which has a positive correlation with the above mentioned two main factors.Simulation results show that the designed irregular B-QC-LDPC codes can make the error-floor at least down to the BER of 10-9 at the cost of 0.2dB performance loss in waterfall region compared with the commercial DVB-S2 irregular LDPC codes with the same code rates and codes length,each of which will exhibit the error-floor phenomenon at the BER of 11-6.In addition,the designed irregular B-QC-LDPC codes with code rates 0.677,0.75,0.8 and 0.833,could achieve 12.65dB,12.15dB,11.8dBand 11.5dB high NCG at the BER of 10-15 when assuming the error-floor of designed irregular B-QC-LDPC codes is lower enough.Compared with the large girth regular B-QC-LDPC code with code rate 0.833 and code length 18360bits,the designed irregular B-QC-LDPC code with the same code rate 0.833 but shorter code length 16200bits can achieve 0.2dB performance improvement.3.Aiming at the problem of that the component code rates can not perfectly match their corresponding sub-channel capacities in the regular B-QC-LDPC code based multi-level coded modulation(MLCM)scheme,we design the irregular B-QC-LDPC code based MLCM scheme to further improve the BER performance of MLCM systems.Since the BER performance of the MLCM system with given modulation format and mapping rule strongly depend on the component code rate assignment and the component FEC codes,then we propose a sub-channel capacity analysis method based on mutual information(MI)and generalized mutual information(GMI)for the MLCM system with aribitrary modulation formats and mapping rules to obtain the theoretical optimal component code rate assignment for the MLCM system.By adopting the well designed sub-channel capacity matched irregular B-QC-LDPC component codes to their corresponding sub-channels of the MLCM system,the BER performance of the MLCM system can be further improved.Simulation results show that the designed irregular B-QC-LDPC code based 8QAM to 64QAM MLCM systems with total code rate 0.75 show the BER performance very close to their corresponding channel capacities,and the distances between the required signal-to-noises(SNRs)at the BER of 10-8 and the channel capacities are 1.08dB,1.18dB,1.26dB and 1.58dB,respectively.In addition,the designed irregular B-QC-LDPC code based 16QAM/64QAM MLCM system can achieve 0.4dB/1.2dB performance improvement compared with the recently proposed regular B-QC-LDPC code based 16QAM/64QAM MLCM system with the same total code rate 0.75 but longer total code length.4.Aiming at the problem of the high decoding complexity of the traditional non-binary QC-LDPC(NB-QC-LDPC)code based CM scheme,we propose a regular NB-QC-LDPC code based MLCM scheme to reduce the decoding complexity of the QC-LDPC code based CM systems while keeping or outperforming its original BER performance.Firstly,we propose a superposition construction based method to construct NB-QC-LDPC code with less number of short cycles and/or possibly enlarged girth.Then,we analyze the changing trend of the BER performance and decoding complexity of the NB-QC-LDPC code defined over the Galois field GF(Q)incident to Q.The decoding complexity increases proportionally with the increase of Q,but the best BER performance usually corresponds to a smaller Q.Finally,by replacing the high-order NB-QC-LDPC code based CM scheme to the low-order NB-QC-LDPC code based MLCM scheme,the decoding complexity can be effectively reduced.Simulation results show that,the designed GF(4)/GF(8)QC-LDPC code based 16QAM/64QAM MLCM system can perform almost the same or even better BER performance with/than the corresponding traditional GF(16)/GF(64)QC-LDPC code based 16QAM/64QAM CM system;Compared with the irregular B-QC-LDPC code based 16QAM/64QAM system,the designed GF(4)/GF(8)QC-LDPC code based 16QAM/64QAM MLCM system show better BER performance in the cost of higher decoding complexity.