Low-Density Parity-Check Codes Decoding And Its Quantization

Low-Density Parity-Check (LDPC) codes are a class of capacity approaching error- correcting codes. By using low complexity sum-product algorithm, LDPC codes can get near Shannon limit decoding performance with almost all errors detectable. For long code lengths, LDPC codes can even outperform Turbo codes. Due to the advantages of LDPC codes, their applications in reliable communications have received great interests and have become one of most attractive field in channel coding community. Now, the application of LDPC has been put on the agenda.This thesis investigates some aspects of LDPC codes with emphasis on message passing algorithms and quantization decoding schemes of LDPC codes. The main results and contents are as follows.1. Based on Tanner graph, the representation and construction of LDPC codes are addressed, and the two decoding algorithm for LDPC codes, i.e, bit-flipping algorithm and sum-product algorithm, are discussed. From two aspects-minimum distance and the failure of independence assumption, the impacts of cycles to the performance of LDPC codes are analyzed.2. The principles of soft decoding and message passing are discussed. Based on Normal graph, the update formulas for message passing are derived and further the optimality of message passing algorithm for cycle-free graphs is proved. Finally, the issues affecting message passing in graphs with cycles are analyzed.3. By theoretical analysis and simulation, quantization decoding of LDPC codes is studied. An efficient quantization-decoding scheme is proposed which can greatly reduce the decoding complexity with a little performance loss.Although long LDPC codes are superior to Turbo codes, it is not the case for short LDPC codes. So the modification of decoding algorithm is essential to the performance improvements for LDPC short codes.