Research On Encoding/Decoding Algorithm And Structure Of Non-binary LDPC Codes

Turbo and low density parity check (LDPC) codes are the best so far in the field of channel coding theories. With similar performance to Shannon limit, they have been applied in various fields of telecommunication. Compared with Turbo codes, LDPC codes become predominant for their low decoding complexity and flexible coding speeds. Non-binary LDPC codes, esp., are more capable of rectifying burst and random noises, are suitable for high-order modulation system and can meet the high requirements of modern telecommunication.There have been sophisticated research about binary LDPC codes such as the coding and decoding algorithms, performance analysis approach and the search approach of the best-degree distribution function based on White Gaussian Noise and Rayleigh fading channels. As for Non-binary LDPC codes, their high complexity limits their application, although many conclusions about binary LDPC codes can be used. Further research should be made about reducing the complexity of the coding and decoding of Non-binary LDPC codes, the best-degree distribution function searching for irregular codes and the construction of parity-check matrix. The paper investigates the decoding algorithms with low computational complexities,best-degree distribution searching algorithms for irregular codes and the application of Non-binary LDPC codes:1. Based on the study of fundamental coding principle for binary LDPC codes and SPA(Sum-Product Algorithm) decoding algorithms and related algorithms in log-domain, several coding algorithms, SPA decoding algorithms and log-domain SPA decoding algorithms are investigated for Non-binary LDPC codes. Non-binary LDPC codes vs. binary LDPC codes in terms of performance are compared by simulation.2. The constructing algorithms for parity-check matrix of binary LDPC including searching algorithms for best-degree sequences and the constructing algorithms for parity-check matrix are investigated. Best-degree distribution sequence under Rayleigh fading channels is provided by DE(Density Evolution) of binary LDPC, Differential Evolution and computer searching; the best regular LDPC codes and irregular binary LDPC codes with best-degree distribution sequences under white Gaussian Noise and Rayleigh fading channels are analyzed and compared through computer simulation. Extrinsic Transfer (EXIT) of binary LDPC codes is investigated and is expanded to the non binary LDPC codes. By this, differential evolution and computer searching, the best-degree distribution sequence for non-regular LDPC codes under white Gaussian Noise channel are provided and the performance of the Non binary LDPC codes is compared by simulation.3. Fast and low complexity decoding algorithms for Non-binary LDPC codes, including the improved SPA decoding algorithms in log-domain, decoding algorithms for Non-binary LDPC codes based on FFT, and the decoding algorithms for Non-binary LDPC based on FFT in log-domain are investigated. As for the complex calculation of parity-check nodes, a decoding algorithms to reduce complexity is presented and simulated, which shows that the performance decreases by 0.3 dB but the decoding complexity is reduced significantly.4. Rectifying burst errors is the biggest advantage of RS codes. By comparison, non binary LDPC codes are more capable in this regard. Hence, to replace RS codes and binary Turbo codes with Non-binary LDPC codes and construct new concatenated code is proposed. The concatenated code needn't interleaver and can overcome interleaving lags because of the interleaving characteristic of non binary LDPC codes. In addition, iteration decoder for LDPC codes and Turbo codes can form the iteration between codes, which improves error rectification.5. As for MIMO-OFDM system, the performance of non-binary LDPC codes esp. the GF(2P) based non-binary LDPC codes used in NLDPC-MIMO-OFDM of MIMO-OFDM system is investigated. The performance of different limit filed NLDPC-MIMO-OFDM under white Gaussian noise and Rayleigh fading channels is compared by simulation and compared with the use of binary LDPC codes in LDPC-MIMO-OFDM systems.