On The Construction Of QC-LDPC Codes

Low-Density Parity-Check (LDPC) codes are one kind of error control codes, whose performance can be near Shannon limit. Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes are one kind of LDPC codes, whose parity-check matrices are with quasi-cyclic style, so their encoding complexity and decoding complexity are low.Major methods for the construction of QC-LDPC codes include Finite Geometry, Balanced Incomplete Block Design and 3D lattice. 3D lattice is one kind of Balanced Incomplete Block Designs, which can get codes with girth 10. Girth and cycles of QC-LDPC codes are important factors, which can affect performance greatly. Generator matrices of QC-LDPC codes are with quasi-cyclic style too, which means the codes can be encoded with shift register. QC-LDPC codes with dual-diagonal parity structure do not have to get generator matrices, so they can perform fast encoding.Adaptive modulation and encoding need length-compatible and rate-compatible QC-LDPC codes. By analyzing cycles of QC-LDPC codes, the writer deduces a theorem and a deduction, and designs two compressing methods based on them. The methods include Recursive-Compressing and Single-Compressing, which can generate codes with continuous length. For the realization of structured puncturing for rate-compatible QC-LDPC codes with dual-diagonal parity structure, the writer ameliorates a method, the advanced method can be more real-time with lower operation complexity than the original method. Besides the methods above, the writer introduces a row-combining method, which can generate codes with compatible rate and constant length.LDPC codes can be used in the area of modern communication systems and memory systems. And also, the writer introduces the application of LDPC codes in quantum communication systems, including two methods to design codes, Balanced Incomplete Block Design and Finite Geometry. Then the writer discusses the problems and probable solutions for LDPC codes used in quantum communication systems.At last, the writer introduces some important points of LDPC codes that are worth studying in the future, including nonbinary LDPC codes, combining with other error control codes, the realization in a system and the application in other subjects.