Performance Analysis And Quantization Decoding Of LDPC Codes

Low-Density Parity-Check (LDPC) codes are a class of capacity approaching error- correcting codes. By using low complexity algorithms based on belief propagation, LDPC codes can get near Shannon limit decoding performance. 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 performance analysis and quantization decoding schemes of LDPC codes. The main results and contents are as follows.1. Based on Factor graph, the representation and construction of LDPC codes are addressed, and the soft decoding algorithm for LDPC codes, i.e., sum-product algorithm and minimum-sum algorithm, are discussed.2. The major factors which impact LDPC codes'performance are summarized. Analyzing the impact of degree distribution on the long-length LDPC codes and introducing the optimized degree distribution algorithm under the AWGN channel based on density evolution or Gaussian approximation and differential evolution. The impact of cycles on the short-length LDPC codes is analyzed and the PEG algorithm is introduced. The ACE algorithm which can degrade the error floor efficiently is introduced.3. 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 good, the encoding problem is hard to solve. So the study of encoding and quantization decoding algorithm is essential to the practical use.