Only since the mid-1990s, with the increase in computational power, has the importance been realized regarding low-density parity-check (LDPC) codes as leading error correcting codes. The work in this thesis primarily studies LDPC codes that are defned by a parity-check matrix comprised of r × r permutation matrix blocks, that is, permutation-block LDPC codes. More specifically, we study their minimum Hamming distance, as this is a parameter that affects the performance of linear codes, and thus LDPC codes. It has been proven that there are upper bounds on the minimum Hamming distance of quasi-cyclic codes, defned by a parity-check matrix comprised of r × r circulant matrix blocks, regardless of how large we allow r. However, we show that if general permutation matrices are used instead of circulant matrices, we are able to exceed the bounds allowed by quasi-cyclic codes. Graphical representations of the codes, called Tanner-graphs, are used in proving many useful results regarding permutation-block LDPC codes and their minimum Hamming distance. We show a characterization of the minimum Hamming distance of these codes and we produce an algorithm for constructing permutation-block LDPC codes with large minimum Hamming distance.
