Abstract
Abstract Low-density parity-check (LDPC) block codes have been shown to have near-capacity perfor- mance with iterative message-passing decoding and su±ciently long block length. However, block codes have the disadvantages in the respect of encoding and decoding complexity. LDPC convolutional codes (LDPC-CCs) are convolutional codes with sparse parity check matrices. They can encode and decode arbitrary lengths of data and can be encoded using shift registers with small complexity. Previous algebraic constructions of LDPC-CCs are all based on their quasi-cyclic LDPC (QC-LDPC) block code counterparts. However, codes of girth 6 may be obtained by previous methods. Therefore, in this thesis, we develop a general- ized construction of LDPC-CCs and girth of the constructed codes is at least 6. Within this set of codes, we propose constructions for LDPC-CCs of girth at least 8. Simulation results show that codes of girth 8 by our construction have performance similar to codes constructed by the previous method. However, computer search is needed for ‾nding codes of girth 8 in previous constructions, while the codes obtained by our constructions are guaranteed to have a girth at least 8. i