A column-weight two parity-check matrix $H$ is represented by a graph known as structure graph. In this thesis, construction and analysis of slope-based low-density parity-check (LDPC) codes having a cylinder structure graph is considered. In particular, design of codes with maximum possible girth is addressed. Depending on the row-weight of $H$, three types of codes referred to a type-I, type-II and type-III codes with maximum girth 16, 24 and 12, respectively, are distinguished. Deterministic low-complexity algorithms constructing such codes are given. The convolutional codes associated with these three types of codes are analyzed and it is shown that the free distance of a so constructed convolutional code is equal with the minimum distance of the corresponding block code. Replacing cylinder structure graphs with the cylinder structure graphs having diameters, we obtain two applied on an AWGN channel and decoded with sum-product iterative decoding algorithm. The definition of structure graphs is extended to a new concept referred to a block-structure graphs representing codes having parity-check matrices with arbitrary column weight and consisting of circulant matrices. Using this and the slope concept, we design codes of girth at most 18. Simulation results confirm that from performance perspective the constructed codes outperform their LDPC pseudo-random counterparts.
