Construction of Protographs for Large-Girth Structured LDPC Convolutional Codes

In this paper, we present a method to construct the girth-6 protographs that lead to the shortest constraint length in the convolutional structure. A stringent structural constraint is imposed on the protographs such that the decoder can be implemented efficiently. Then, given the structural constraint, it is shown that finding the aforementioned protographs is equivalent to solving a simple algebraic problem. Based on this mathematical formulation, the girth-6 protographs are created without complicated graph search, from which we derive good low-density parity-check (LDPC) convolutional codes by using periodic quasi-cyclic lifting. The performance of such constructed codes are presented in comparison to the AR4JA-based LDPC convolutional codes.