Research On Low-Density Parity-Check Codes And Their Applications

Error-correcting codes are widely applied in many fields, such as mobile communications, satellite communications, optical communications and disk recorders. Low-density parity-check (LDPC) codes belong to error-correcting codes approaching Shannon limit.The construction methods of LDPC codes and their applications are studied in this dissertation. Several types of quasi-cyclic regular codes and an irregular code are proposed through restricting the girth of Tanner graph, which enable easy encoding. These codes are applied in wireless LAN with one antenna and multi-antennas. It is found that these codes outperform some comparable codes not only in AWGN channels but also in Rayleigh fading channels.Firstly, based on cyclic difference sets of combinatorics,a new method for constructing LDPC codes is proposed. This method can generate a large number of regular LDPC codes with constant row weight and constant column weight. We call them CDS-LDPC codes. And this method could eliminate the cycles with length equal to four and decrease the ones with length equal to six. Sum-product decoding algorithm is used to decode CDS-LDPC codes and simulation results show that they exhibit good performance.Secondly, a novel construction from shifted identity matrices using several inequalities is presented to generate Tanner graphs with girth 8, 10 and even 12. The codes from this method are called SIM-LDPC codes, which extend those codes based on permutation matrices in exiting literatures. SIM-LDPC codes have various code rates and code length, ranging from low to high. They perform well with iterative decoding.Thirdly, a novel and simple construction of regular LDPC codes is proposed, which uses sparse binary sequences. These LDPC codes are called SBS-LDPC codes. The distribution matrix of ones in parity-check matrix is introduced into the new construction. The cyclic cross-correlation function and the cyclic auto-correlation function are utilized to ensure that the girth of Tanner graph was eight. The new codes perform well using the sum-product algorithm for iterative decoding.Low encoding complexity can also be achieved due to the inherent quasi-cyclic structure of the SBS-LDPC codes, SIM-LDPC codes and CDS-LDPC codes.Lastly, the applications of LDPC codes are studied. The performance of SIM-LDPC codes is further investigated in fading channels. The OFDM system is used insimulations and the parameters are selected according to IEEE 802.11a standard. A type of practical irregular LDPC codes is designed and simulated. The MIMO-OFDM system is adopted in simulations and the parameters are chosen from IEEE 802.11n standard. The results show that two types of LDPC codes perform well in their respective application environments.