Research On Theory Of LDPC Codes

Robert Gallager in 1960's introduced Low-Density Parity Check (LDPC) codes.Due to the decoding complexity, they had been forgotten for about 30 years until they were rediscovered in late 1990s. Recently, many researchers extensively studied LDPC codes and designed a good code which approach Shannon limit as close as 0.0045dB.LDPC codes with the belief propagation (BP) decoding based on tanner graph provide much powerful error correcting capability. Moreover, compared to maximum likelihood (ML) decoding, the decoding complexity has been significantly reduced. Therefore, LDPC codes were applied to the next generation wireless communication systems such as DVB-S2,WIMAX, etc.In this paper, a stopping criterion for irregular LDPC decoding is proposed.This scheme considers the decoding property of irregular LDPC codes and decides whether iterative decoding continues based on the log-likelihood ratio value of lowest degree variable nodes.Compared with existed schemes, this scheme decreases the mean iteration times of decoding and reduces computation complexity with slight performance degradation.At very low SNR, residual frequency and phase offset will make obvious degradations on the LDPC decoding performance, so,a carrier refiner is required with iterative decoding.A code-aided iterative carrier estimation is proposed based on statistics of soft information from LDPC iterative decoder. An early synchronization stopping that uses feedback from LDPC decoder is proposed.The proposed scheme makes use of the variations of the number of satisfied parity-check constraints to early stop iterative synchronization.The simulation results show that the proposed method decreases the complexity greatly by avoiding unnecessary iterative synchronization under little performance degradation.