Research On Encoding And Decoding Technology And Application Of LDPC Codes

Low-density parity-check (LDPC) codes are a class of linear block codes which are defined bysparse matrixes or bipartite graphs．LDPC codes have many advantages, such as easily described,Shannon limit approaching performance by using iterative decoding algorithm and decoding easilycompleted in low complexity. Therefore, it becomes a hot topic in the error correction coding field.Based on deeply understanging of encoding principle, the construction methods of checkmatrix and iterative decoding algorithm, the structural construction methods of LDPC codes anddecoding algorithms are studied in the paper, and in the PCM/FM telemetry system simulation andanalysis of proposed and improved methods is carried out. The main works are summaried asfollows:1. Random construction methods of LDPC codes are hard to practical application, so focusingon the structural construction methods. Based on studying properties of optical orthogonal codesand theories of quasi-cyclic LDPC codes, a method of constructing quasi-cyclic LDPC codes isproposed, which do not include cycles of length 4 and 6 in their check matrixes. Simulation resultsshow that the new method is superior to the method which is proposed by Mackay. And due to it hasthe characteristics of quasi-cyclic LDPC codes, it is more conducive to hardware implementation;2. Based on the quasi-cyclic LDPC codes constructed by optical orthogonal codes, a method ofconstructing irregular LDPC codes is proposed by introducing quasi-diagonal matrix. The methodcan reduce the encoding complexity further and improve the decoding performance. And themethod can optimize degree. Simulation results confirm its good decoding performance;3. By studying the relationship between checksum and error bits, and their changing patterns,when BP algorithm used in decodeing the short and middle length LDPC codes, a new method forearly stopping decoding iteration is proposed to improve the decoding efficiency. At the same time,when information is passed between check nodes and variable nodes, the oscillation occurs. A newmethod is proposed to amend negative impact of the phenomenon. Simulation results show that thenew decoding algorithm improves the decoding performance, reduces the number of iterationssignificantly when SNR is low;4. Due to the min-sum decoding algorithm using approximate computation, which resultsin the decoding performance reducing, a new improved min-sum decoding algorithm is proposed.Simulation results show that the improved method has similar performance with BP algorithm, butits implementation complexity is lower;5. In the PCM/FM telemetry system model which based on LDPC codes, the proposed methods of construction LDPC codes and improved decoding algorithms are simulated andanalysed, then comparing with the traditional methods. The results show that in the system theproposed and improved methods have much better performance.