Constructions And Decoding Implementations Of Fast Convergence Quasi-Cyclic LDPC Codes

Low-density parity-check (LDPC) codes are Shannon limit approaching codes, having many advantages, such as low decoding complexity, low error floor and so on. Error control using LDPC codes is currently the most promising coding technique to achieve Shannon capacity for a wide range of channels, and applies to many systems successfully. Quasi-cyclic (QC)-LDPC codes are a branch of LDPC codes. QC-LDPC codes can be encoded with some simple accumulator registers, due to the quasi-cycle characteristic, greatly reducing their encoding complexity. QC-LDPC codes inherite many outstanding features from LDPC codes. Meanwhile, QC-LDPC codes dramatically improve their decoding speed by using parallel or quasi-parallel decoding architecture. Therefore, QC-LDPC codes have a very high research value.Firstly, the study includes LDPC constructions based on finite fields. On constructing basis matrices based on the basic structures of a finite field properly, the null spaces of the parity check matrices corresponding to the basis matrices give some good codes, which have large minimum distances, large trapping sets and no short cycles (especially cycles of length4). The codes with these characteristics tend to have low error floors and fast convergence iterative decodings. Therefore, we look for approaches to construct basis matrices, which give codes with the above characteristics, based on the structural characteristics of finite fields and prime fields.Two basis matrices are constructed based on the features of prime fields. Then two parity check matrices are obtained by using additive array dispersions. We notice that the two classes of QC-LDPC codes constructed here have relatively large minimum distances. Simulation results show that codes constructed in these two approaches have Shannon limit approaching performances, and have no visible error floor in all simulation regions. We also find a LDPC code with a fast convergence characteristic.Three basis matrices are constructed based on the features of finite fields. Then three parity check matrices are obtained by multiplicative array dispersions. We notice that the three classes of QC-LDPC codes constructed here also have relatively large minimum distances. Simulation results show that the codes have advantages in some aspects of code performances, compared with the MacKay codes with similar lengths and rates. We also notice that the codes have ultra low error floors.