Research On The Construction Of QC-LDPC Codes Based On Quadratic Residue Codes And Encoding Implementation

Since Mackay and Neal rediscovered that the performance of low density parity check(LDPC)codes could approach to the Shannon limit in 1996,LDPC codes have been widely used.But in order to lower the complexity of encoding and decoding,and simplify the hardware implementation,quasi-cyclic LDPC(QC-LDPC)codes are usually considered in real systems.Quadratic residue(QR)code is a kind of linear block code in finite field with good performance.Based on the algebraic structure of QR codes and algebraic construction algorithm of LDPC codes,a new class of QC-LDPC codes is constructed in the thesis,referred to as QR-QC-LDPC codes.This paper explains the structure of QR code in commutative algebra GF(2)[x]/(x~p-1)first and then demonstrates a new form of check matrix of QR code in finite field using cyclic code zero theory.QR-QC-LDPC code is constructed using the new check matrix as the base matrix.Considering the girth of LDPC code is vital to its performance,the paper proves the girth of QR-QC-LDPC code is at least 6,which ensures good error rate of QR-QC-LDPC code in theory.Meanwhile,we can obtain the QR-QC-LDPC codes with different length and varying rate when choosing different QR code or using different size submatrix of QR-code check matrix as the base matrix for construction.The simulation results indicate that the performance of QR-QC-LDPC codes can reach to progressive edge-growth(PEG)LDPC codes,even overpass them in some QR-QC-LDPC codes.Practical systems usually adopt QC-LDPC code,so QR-QC-LDPC code whose performance reaches PEG code is promising in application.Furthermore,to speed up the encoding of QR-QC-LDPC code in simulation,the paper gives a GPU-based encoding solution of parallel processing with high throughput for any QC-LDPC code.According to the quasi-cyclic check matrix of QC-LDPC code,the paper first introduces its generator matrix with quasi-cyclic structure as well.Then an encoding solution with the throughput of gigabit per second is designed based on the quasi-cyclic property of the generator matrix and the structure of the threads and memory in GPU.In the simulation,three different length QC-LDPC codes are tested and all their encoding rates reach 10 Gbps and the encoding speed outperforms the compared GPU encoder;when encoding(1944,1620)QC-LDPC code of 802.11ac standard,our encoder increases by 1.9Gbps in throughput compared with the CMOS encoder;when encoding the four codes of WIMAX standard,our encoder is 3.94 to 7.73 times the throughput of the FPGA encoder.