Research On Design And Performance Of GLDPC Codes Based On Quadratic Residue Codes

A low density parity check(LDPC) code can be viewed as a concatenated code consisting of repetition codes and single parity check(SPC) codes.Researchers found that a better code called a generalized LDPC(GLDPC) code can be constructed by replacing SPC codes in LDPC codes with component codes with more powerful error correction capability.Quadratic residue(QR) codes are a kind of short codes which have larger minimum Hamming distances than general block codes,and thus their error correction performance is better.In view of this,this thesis uses QR codes as the component codes to design GLDPC codes.The main contributions are as follows:1.After studying the traditional construction method of GLDPC codes(denoted by method 1) and the performance of Hamming-GLDPC codes constructed by method 1,this thesis proposes a new construction method of GLDPC codes based on QR codes(denoted by method 2),the corresponding codes are called QR-GLDPC codes.Then we simulated and analyzed the different code length of QR-GLDPC codes at the same code rate,the same code length of QR-GLDPC codes at different code rate and the traditional LDPC codes.Moreover,compared to the Hamming-GLDPC codes constructed by method 1,the performance of the Hamming-GLDPC codes reconstructed by method 2 is significantly improved;2.In order to further improve the performance of the GLDPC codes,a method for constructing GLDPC codes based on an optimized 4-ring distribution is developed(denoted by method 3).Simulation results demonstrate that QR-GLDPC codes and Hamming-GLDPC codes constructed by method 3 are superior to those based on method 2.3.GLDPC codes based on different component codes(Hamming codes,QR codes) are analyzed from decoding complexity point of view.Simulation results show that QR-GLDPC codes are better than Hamming-GLDPC codes with same lengths and rates when signal-to-noise-ratio(SNR) is larger than 4dB.Before 4dB,Hamming-GLDPC codes are better.However,it is at the cost of decoding complexity,that is,the number of replaced component codes is several times the number in QR-GLDPC codes.