Abstract
Low-density parity-check (LDPC) block codes have been shown to have near-capacity perfor- mance with iterative message-passing decoding and sufficiently long block length. However, quite a number of methods for designing LDPC block codes are based on random construc- tions; the lack of structures leads to serious disadvantages of high complexity in encoding and decoding. Therefore, in recent researches, codes with algebraic structures have been devel- oped, among which quasi-cyclic LDPC (QC-LDPC) codes are an important class. They can be encoded and decoded with low complexity, suitable for many applications such as packet- switching networks. In this dissertation, we first develop new constructions of QC-LDPC codes with good distance and girth properties. Simulation results show that the constructed codes can have better error performance than previous codes at high signal-to-noise ratios. Constructions of unequal error protection (UEP) QC-LDPC codes are also provided in this dissertation. A criterion for constructing UEP QC-LDPC codes via the masking technique is given, based on which explicit conditions on the base parity-check matrices and masking matrices are provided. Three specific constructions of UEP QC-LDPC codes are also presented. Furthermore, a sufficient condition to ensure strict UEP is developed. Simulation results show that the constructed UEP codes can indeed provide coded bits with different protection levels and perform better than traditional time-sharing schemes. Finally constructions of variable-rate UEP QC-LDPC codes are developed. The criteria which guarantee that a higher-rate QC-LDPC code can be obtained by adding column-blocks to or removing row-blocks from the parity-check matrix of a given lower-rate QC-LDPC code are provided. Then the conditions on the base parity-check matrices and masking matrices are given. We also present specific constructions of variable-rate UEP QC-LDPC codes. Simulation results show that all the constructed codes can indeed provide coded bits with different error-correcting capabilities and have good error performance.