Research On Construction Method Of QC-LDPC Codes Based On Cycle Difference Families

Quasi-Cyclic Low Density Parity Check?QC-LDPC?codes are special subclass of LDPC codes with quasi-cyclic characteristics.Cyclic Difference Family?CDF?is an important basic theory in combinatorial mathematics,which can be used in construction of QC-LDPC codes with better performance.Therefore,three construction methods based on cyclic difference family was proposed in this thesis,and the main works are presented as follows:1.To address the issue that the girth of Type-I QC-LDPC code currently exists is relatively small,a code construction method based on the cyclic difference family is proposed.The designed code with a girth of at least 8 has an approximate double diagonal structure,and has better error correction performance.The simulation results show that when the code-rate is 0.5 and the bit error rate is 10^-6,the Net Coding Gain?NCG?of CDF-Type-I QC-LDPC?1332,666?code based on cyclic difference family has respectively increased by 0.10dB,0.12dB and 0.13dB,than those of the GCD-Type-I QC-LDPC?1430,715?code based on the Greatest Common Divisor?GCD?,PEG-Type-I QC-LDPC?1332,666?code with Progressive Edge Growth?PEG?and SD-Type-I QC-LDPC?1332,666?code based on the SIDON sequence?SD?.2.In view of the problem that the choice of the current code-length and the code-rate is not flexible enough,a method of constructing irregular Type-I QC-LDPC code based on a perfect cyclic difference family is proposed.The perfect cyclic difference family is applied to the design of the check matrix,thereby constructing an irregular PCDF-Type-I QC-LDPC code,and the code-length and code-rate of the code can be flexibly selected.The simulation results show that in this thesis,the irregular PCDF-Type-I QC-LDPC code based on the perfect cyclic difference family constructed has better error correction performance.3.When the minimum distance and the girth are small,the error correction performance of the code will be seriously reduced.In order to solve this problem,a method of constructing irregular Type-II QC-LDPC code based on perfect cyclic difference family is proposed.The parity check matrix constructed by this method consisting of zero matrix,weight-1 cyclic matrix and weight-2 cyclic matrix,not only makes the constructed code girth at least 8,but also reserves the advantage of Type-II QC-LDPC code,with a higher minimum distance upper bound.The simulation results show that when the BER is 10^-6,compared to the irregular PCDFK-Type-II QC-LDPC?4788,2394?code with fast-encoding characteristic based on perfect cyclic difference family,and the regular PCDF4-Type-II QC-LDPC?3906,1953?code with column weight of 4 constructed based on perfect cyclic difference family,the NCG of the irregular PCDF-Type-II QC-LDPC?3856,1928?code has an increase of 0.42dB and0.15dB,respectively.In summary,the QC-LDPC codes constructed in this thesis based on the cyclic difference family and the perfect cyclic difference family have powerful iterative decoding performance and avoid error floor,which has important theoretical significance and practical reference value.