Research On The Construction Of Structured Low-Density Parity-Check Codes With Large Girth

As an important class of linear block codes defined by sparse matrices, low-density parity-check (LDPC) codes have been considered as a class of codes with near Shannon limit performance under belief-propagation decoding algorithms, such as SPA. It is highly desirable to construct LDPC codes with excellent performance and compact description, as well as enough structures suitable for implementation, from the theoretical and application perspective, collectively. This dissertation investigates the issue of constructing structured LDPC codes with large girth. The major contribution of this paper is listed as follows.1) Three classes of structured regular girth-6+ LDPC codes are constructed from frequency-hopping patterns. The new codes perform very similar to the randomly constructed LDPC codes over the AWGN channels.2) Two classes of girth-6+ QC-LDPC codes are proposed by doubly-extended RS codes and cyclic MDS codes.These codes perform well over the AWGN channels.3) A general framework is proposed by generalized RS (GRS) codes to construct binary and nonbinary LDPC codes. Ten classes of well-known methods can be elegantly and uniformly derived from the GRS-based framework.Base on the framework, the essential property these methods invariably pursue (i.e. girth at least 6) is trivially and simply satisfied.4) Two classes of girth-8+(3,L) QC-LDPC codes are presented by B2(mod m) sequences. For m prime, codes in the first class perform better than the PEG-LDPC codes. Codes in the second class perform nearly as well as the PEG-LDPC codes.5) A deterministic method is presented to construct girth-8 (3,L) QC-LDPC codes and girth-8 (4,L) QC-LDPC codes.Using these two types of girth-8 codes as component codes in the construction method based on the Chinese remainder theorem (CRT), a new class of girth-8+ combined QC-LDPC codes is constructed with flexible block lengths. The new combined codes perform very well over the AWGN channels.6) For an arbitrary girth-10+(3,L) QC-LDPC code and a special class of girth-12 (3,L) QC-LDPC code, two tight lower bounds of the consecutive lengths are presented.Combined with B2(mod m) sequences, a efficient method is presented to construct girth-10+ and girth-12 (3,L) QC-LDPC codes.Furthermore, a constructive proof is presented for the existence issues of a large variety of girth-10+ and girth-12 (3,L) QC-LDPC codes.