Research On Encoding/Decoding Of LDPC Codes And Code-aided Carrier Synchronization

Low-density Parity-check (LDPC) Code is an class of advanced channel coding. When decoding under belief propagation (BP) algorithm, it can achieve the performance of nearing Shannon limit. LDPC codes can be divided into binary LDPC codes and non-bianry LDPC (NB-LDPC) codes. This thesis studied the encoding and decoding algorithms of binary LDPC codes at first. And on this basis, the construction methods and decoding methods of NB-LDPC codes were investigated. Considering that the decoding messages of BP decoding contain a lot of probability information, we provided a code-aided iterative carrier synchronization algorithm for the NB-LDPC coded system. Meanwhile, the corresponding equations were derived and the simulations were presented.The main works are as follows:(1) The basic concepts of LDPC code were introduced. In order to implement the LDPC encoding system conveniently, the parity-check matrix which has the dual diagonal structure and the fast encoding algorithm were researched. Then we studied the BP decoding algorithm and its improved algorithm. And about the decoder, we investigated the full parllel structure and the node grouping structure. Furthermore, the decoding performance of various decoding algorithm and decoding structure were analyzed.(2) Using C and MFC as the development platform, we designed and implemented a simulating and testing software of LDPC codes. The software was divided into four modules:encoding modual, modulation and transmission modual, decoding modual and simulation testing module. The encoding part supported 19 code-length,6 code-rate of LDPC codes, which was provided by IEEE 802.16e standard. The modulation and transmission part supported four kinds of modulation:BPSK, QPSK,16QAM and 64QAM. The decoding part supported two kinds of decoding algorithm and two decoding structures.(3) In the design and implementation of LDPC decoding process, this thesis proposed a message storage strategy and the corresponding decoding implementation process. When decoding with the soft decision algorithm, only the messages corresponding to the non-zero elements of the parity-check matrix were stored. The proposed method can save the storage space and improve decoding speed.(4) With the introducion of the basic concepts of finite field, the method of constructing finite field was described, as well as the method of realizing the finite field by using the software. Based on the study of several construct methods of NB-LDPC codes, the iterative NB-LDPC decoding algorithm and the fast algorithm based on the FFT were investigated.(5) A code-aided iterative carrier synchronization method based on the expection maximization (EM) algorithm was researched. We studied the code-adid iterative carrier phase synchronization algorithm of binary LDPC code system with high order modulation and proposed an EM-based iterative carrier phase estimation algorithm for NB-LDPC coded system. The form of carrier phase estimation of NB-LDPC coded system was derived. Then the synchronization algorithm was given in this thesis. And the simulation results showed that as long as meeting the convergence condition of the estimator, it can almost achieve the performation of ideal synchronization system.