Research On The Algebraic Construction Method Of LDPC Codes In Optical Communication Systems

With the increasing progress of the information society, the demand of thebandwidth for a variety of the present video business and the just commercialized4G isgreatly increasing, and then the requirement of the large transmission capacity in opticalcommunication systems is increasingly enhanced. For this reason, nowadays thegreatest challenge for high speed optical transmission technique turns out to be how toachieve the optical transmission with the high reliability, long distance, high capacityand low cost. The channel coding technique is an efficient method to increase thereliability. As one of the most important code type, the Low-density Parity-check(LDPC)code has become a research hotspot among the channel coding technique due to itsbetter error-correction performance. The Quasi-cyclic Low-densityParity-check(QC-LDPC) code is a kind of the LDPC code with the flexible selectioncode-length and code-rate as well as the lower coding complexity which has a morepractical prospect in optical communication systems. Therefore, the algebraicconstruction method of LDPC codes for optical communication systems is deeplystudied in this dissertation.This subject is studied under the condition of taking the Natural ScienceFoundation of CQ CSTC (No.2010BB2409):"Study on the novel structure mechanismof the SFEC code type for the high-speed optical communication systems" as theapplication background. The main achievements in this dissertation are as follows:(1) The LDPC fundamental theory including its encoding and decoding theory aresystematically analyzed, then dominant factors which determine the error-correctionperformance of the LDPC code are verified by the simulation test. In addition, after thenoise analysis aimed at each module in the optical communication system, a simulationplatform for optical communication systems involved in this dissertation is built withthe assistance of MATLAB. These works lay a solid foundation for both the laterresearch on algebraic construction method of LDPC codes and the correspondingsimulation analysis.(2) Considering the requirement of the high code-rate in optical communicationsystems, a novel construction method based on the finite field multiplication group andits cyclic subgroups is proposed for QC-LDPC codes. The regular QC-LDPC(5344,4955) code to be suitable for optical communication systems is constructed by the novel construction method,. The simulation results show that the error-correction performanceof the novel regular QC-LDPC（5334,4955）is superior to those of the RS (255,239)code in ITU-T G.709and the LDPC (32640,30592) code in ITU-T G.975.1. The novelregular QC-LDPC（5334,4955）is1.64dB distance from the Shannon Limit, its netcoding gain(NCG) were improved about1.61dB and0.90dB respectively at the bit errorrate(BER) of10-6, Thus the regular QC-LDPC (5344,4955) code is more suitable foroptical communication systems.(3) A novel construction method of LDPC codes to meet the row-column constraintcondition, based on their inverse element characteristic in finite field, is proposed and anovel structure of the parity check matrix is obtained after the fundamentalcharacteristic of the finite field is further studied. Combined with the constructionmethod based on finite field, extracting a sub-matrix in the parity check matrix, aregular QC-LDPC (5344,4962) code suited for optical communication systems can beconstructed after expansion of columns and rows. The simulation results show that theerror-correction performance of the regular QC-LDPC (5344,4962) code by thecode-rate of0.93is superior to the RS (255,239) code and LDPC (32640,30592) code,and the net coding gain is improved about1.77dB and1.06dB respectively at the biterror rate of10-6, which is also improved by about0.16dB when compared with theregular QC-LDPC (5344,4955) code. Therefore, the structure of the QC-LDPC (5344,4962) code can be considered as a candidate code type of super FEC codes used inoptical communication systems.(4) The improving scheme of QC-LDPC codes based on the masking technique isfurther probed in this dissertation after the accomplishment of constructing the regularQC-LDPC code on the basis of finite field. A masking matrix selection scheme aimed atimproving the error correction performance of the LDPC code is presented. In thismasking matrix selection scheme, the nodes, which are searched by the computer, havethe significant effect on the number of girth-6in a basic matrix. This scheme candecrease the amount of girth-6and in order to improve the error correction performanceof LDPC codes by means of setting zeros to some nodes through masking technique.The parity check matrix, constructed by the above construction method based on finitefield, is repeatedly improved by using the masking matrix selection scheme proposed inthis dissertation. The first masking procedure and the second one are effectively reducethe number of the girth-6of the parity check matrix and also improve the error-correction performance of QC-LDPC codes constructed by the parity check matrixof the new. After the first masking procedure, the number of girth-6in basic matrixreduced128. The error correction performance of the novel constructed regularQC-LDPC (5334,4962)-masking-1code is superior to the code before maskingprocedure, both of the codes are at the same code rate and the NCG were improved byabout0.23dB at the BER of10-6. The simulation result verifies the feasibility of theproposed masking scheme in the dissertation and the proposed masking scheme playsan important role in studying the masking technology.