Type-III LDPC Convolutional Codes

A class of geometrically structured quasi-cyclic low-density parity-check codes with a cylinder structure graph and girth 12 is considered. The parity-check matrix of such a code consists of blocks of zeros and cir-culant permutation matrices. A class of convolutional codes is assigned to these codes. The convolutional form generator matrix of these codes is obtained by elementary row and column operations. It is shown that the free distance of the obtained convolutional codes is equal to the minimum distance of their bock code counterparts