Research On The Construction Method Of QC-LDPC Codes Based On Fibonacci-Lucas Sequence

The error correction performance of Low-Density Parity-Check?LDPC?codes can approach the Shannon limit.Research on the construction method of Quasi-Cyclic LDPC?QC-LDPC?codes is the focal point about LDPC coding research.QC-LDPC codes are more convenient to implement which can save a lot of storage space in the hardware implementation process compared with the randomized LDPC codes,In addition,QC-LDPC codes can very well use algebra theory and geometric theory knowledge to construct LDPC codes with excellent error correction performance,and QC-LDPC codes have been used in many communication standards such as IEEE802.16e,CCSDS,WiMAX and GB20600.Referred to the many literatures on the study about construction method of QC-LDPC codes,the QC-LDPC codes can be constructed which have flexible code-length and code-rate,lower coding complexity and great error correction performance based on Fibonacci-Lucas sequence.The research on the construction method of QC-LDPC codes mainly solves these current existing problems that the coding complexity is high and the error correction performance is poor caused by the short cycles and the short minimum distance in this thesis,the main work is as follows:1.In order to optimize the error correction performance caused by the short cycles,a construction method of large girth QC-LDPC codes based on Fibonacci-Lucas sequence is put forward in this thesis.An exponential matrix can be constructed by the special properties of Fibonacci-Lucas sequences combined with a triangular rotation construction method,then,the check matrix can also be constructed by related extended operations of unit matrix and Circulant Permutation Matrix?CPM?.Code-length and code-rate are flexible by setting the index of rows and columns.The check matrix does not have girth-4 and girth-6,and it has excellent error correction performance.The channel environment is the additive white Gaussian noise channel,the modulation mode selects the binary phase shift keying,the decoding mode selects the BP iterative decoding algorithm,and the iteration number is fifty.The simulation result shows that at the Bit Error Rate?BER?of 10^-6,the Net Coding Gain?NCG?of the?2700,1352?F-L-QC-LDPC code is about 1.0dB and 1.6dB more than those of the?2700,1352?F-QC-LDPC code and?2700,1353?L-QC-LDPC code.The NCG of the?2580,1292?F-L-QC-LDPC code is about 1.0dB more than that of the?2580,1292?APS-QC-LDPC code at the same condition.In addition,the computational complexity of these coding methods is proportional to the square of the code-length,and the number of required storage parameters is equivalent.2.In order to optimize the error correction performance caused by the high coding complexity,a rapid coding construction method of QC-LDPC codes based on Fibonacci-Lucas sequence is put forward in this thesis.The check matrix structure is shaped likeH?28?[H₁ H₂],and the right side is a quasi-double diagonal structure which is based on the first construction method.The final check matrix can code rapidly and avoid the girth-4.The simulation result shows that at the BER of 10^-5,the NCG of the?4977,3318?F-L-QC-LDPC code is about 0.3dB and 0.08dB more than those of the?4665,3114?QC-LDPC code based on deleting check matrix row and the Type-II CDS-QC-LDPC code.In addition,the computational complexity of the Type-I F-L-QC-LDPC is proportional to the code-length and the number of required storage parameters is equivalent.3.In order to optimize the error correction performance caused by the short minimum distance,a construction method of Type-II QC-LDPC codes based on Fibonacci-Lucas sequence is put forward in this thesis.Code-length and code-rate are flexible by setting the index of rows and columns,the check matrix increases the minimum distance and avoids the girth-4,it can reduce the generation of large girth with good error correction performance to a certain extent.The simulation result shows that at the BER of 10^-6,the NCG of the?3650,2192?Type-II F-L-QC-LDPC code is about 0.2dB and 0.12dB more than those of the?3650,2192?Type-II CDS-QC-LDPC code and?3650,2192?Type-II S-QC-LDPC.In addition,the number of required storage parameters is equivalent and the computational complexity of these coding methods is proportional to the square of the code-length which are based on the generate matrices.