Performance Comparison Between Non-Binary LDPC Codes And Reed-Solomon Codes

Non-binary low density parity check (Q-LDPC) codes are investigated and compared with binary LDPC (B-LDPC) codes and RS (Reed-Solomon) codes in this thesis. Simulation results indicate that Q-LDPC codes are very effective against noise bursts and fading, especially with high rates. Q-LDPC codes perform 2.7dB better than the conventional RS codes at a frame error rate (FER) of FER=10-4 over noise bursts channels with burst length up to 144bits, and even outperform the soft-decoding RS codes by 7.1dB at FER=10-4 over fast Rayleigh fading channels. It is of significant value for Q-LDPC codes to be applied in future digital communication systems.This thesis is organized as follows. SectionⅠgives a brief introduction of LDPC codes. SectionⅡpresents the encoding and decoding algorithm of B-LDPC codes, including the construction of parity check matrix H, classic decoding algorithm and modern belief propagation decoding algorithm. SectionⅢintroduces a new decoding algorithm with reduced-complexity and an optimized encoding scheme for Q-LDPC codes, and the performances of Q-LDPC codes over noise bursts channels are also discussed. The encoding and decoding scheme of RS codes is introduced in sectionⅣ. SectionⅤdiscusses the application of extrinsic information transfer (EXIT) chart for LDPC codes. SectionⅥprovides the simulation results of Q-LDPC codes, B-LDPC codes and RS codes over additive white Gaussian noise (AWGN) channels, noise bursts channels, and fast Rayleigh fading channels. Conclusion and future work are showed in sectionⅦ.