Construction And Analysis Of Generalized LDPC Codes Based On QR Codes

Low Density Parity Check（LDPC）code is a type of linear block codes with sparse characteristic.Because of its excellent performance being close to the Shannon limit,many scholars have done researches on it.Currently,LDPC codes have been widely used in many systems,such as mobile communication systems and data storage systems.However,there are still many LDPC codes'related areas that are worth exploring further.In this thesis,the following research is carried out on how to reduce the error floor of LDPC codes:1.In order to mitigate the error floor of LDPC codes,this thesis proposes a novel construction method of generalized LDPC codes based on Quadratic Residue（QR）codes.The Quadratic Residue code is a type of linear block codes with beautiful mathematical structure.Under the same or similar code length,it has a larger minimum Hamming distance than the Hamming code,Reed-Muller code and other block codes,so it has more strong error correction ability.By selecting some variable nodes of the original LDPC code as the information bits of the QR code and then adding the check bits of the QR code,a generalized LDPC code is constructed.Compared with the performance of original LDPC codes with different code lengths,the performance of generalized LDPC codes is better.2.In order to further improve the performance of generalized LDPC codes,this thesis proposes a variable node selection algorithm based on trapping sets.By completing the trapping set database of the original LDPC code,the dominant trapping set is selected,and then the variable nodes are selected to optimize the construction of the generalized LDPC code.In addition,a two-stage decoding strategy for this code is also designed.The simulation results show that the above mentioned construction method and decoding strategy can effectively improve the performance of generalized LDPC codes.3.For some LDPC codes,although the above methods have a significant improvement in performance,it is found that there is still a large optimization space.In order to further improve the performance of the generalized LDPC code,this thesis proposes an optimization method by connecting the variable nodes of the QR code check part with the partial check nodes of the original LDPC code,so as to improve the reliability the variable nodes of the QR code check part.Besides,it can have the correct information passed through more paths for propagation.So this thesis proposes a check node selection algorithm based on trapping sets.The simulation results show that the bit error rate of the original LDPC code,whose length is 408 and code rate is 0.5,can only reach9.36368?10^-8 under the signal-to-noise ratio of 5.5dB,and the bit error rate of the improved generalized LDPC code,whose length is 416 and code rate is 0.5,can reach the magnitude order of10^-10.