A Combining Method of Structured LDPC Codes from Affine Permutation Matrices

In this paper we present a class of structured low-density parity-check (LDPC) codes from affine permutation matrices, called the APM-LDPC codes, which are a generalization of quasi-cyclic LDPC codes. We give a necessary and sufficient condition under which an APM-LDPC code has a cycle and introduce a simple method to construct APM-LDPC codes of large length by combining those of small length based on the Chinese remainder theorem. In particular, we show that the girth of APM-LDPC codes obtained in this method is always larger than or equal to those of given APM-LDPC codes