Optimization Design And Performance Analysis Of Generalized LDPC Codes Based On QR Codes

Low density parity check(LDPC)codes are a type of linear block code with sparse parity check matrices,which have been proven to be another type of error correction code close to the Shannon limit after Turbo codes.A quasi cyclic low density parity check(QC-LDPC)code is a structured LDPC code.The quasi-cyclic structure makes its encoding and decoding more flexible,so QC-LDPC codes were usually selected in actual systems.However,there are still many problems for QC-LDPC codes to be explored,such as the high error floor due to the existence of the trapping sets.Therefore,in this thesis,the following research was carried out on how to reduce the error floor of QC-LDPC codes:1.The QC-LDPC codes based on the quadratic residue(QR)codes(denoted as QR-QC-LDPC)have a girth at least 6,and their performance are similar to the random LDPC codes constructed by the progressive edge growth(PEG)algorithm.However,there exists a large number of length-6 cycles in QR-QC-LDPC codes.Therefore,this thesis developed a masking algorithm based on trapping sets and length-6 cycles information to optimize the QR-QC-LDPC codes.Simulation results show that a gain of approximately 1 d B can be obtained through masking optimization.2.In order to further improve the performance of the QR-QC-LDPC codes,this thesis proposed to use the QR code and the QR-QC-LDPC code as the component code and the global code to construct generalized low density parity check(GLDPC)codes.Therein,the Tanner graphs of an LDPC code and a QR code were integrated as a whole and the encoding can be done by treating the GLDPC code as a new linear block code.The information bits of the component code all come from the variable nodes of the global code.Moreover,this thesis designed an algorithm for selecting variable nodes based on the trapping sets.Simulation results demonstrat that this method of constructing GLDPC codes has a good performance with a small rate loss.3.For the constructed GLDPC code,a two-stage decoding algorithm was developed.This algorithm utilizes the characteristics of low error floor and large Hamming distance of the QR code.The correct information in the QR code is transmitted to associated variable nodes of the global code,and then is propogated to all variable nodes and check nodes,thereby achieving the purpose of correcting errors.Simulation results show that,compared with the optimized QR-QC-LDPC code,the resultant GLDPC code obtains a gain close to 0.3 d B with a rate loss of about 0.05.