A New Construction Method for Large Girth Quasi-Cyclic LDPC Codes with Optimized Lower Bound using Chinese Remainder Theorem

This paper presents a new construction algorithm of Quasi-cyclic low-density parity-check (QC-LDPC) codes of medium to large block-length by combining QC-LDPC codes of small block-length as their component codes, via Chinese remainder theorem. Such component codes were constructed by permuting each column block sequentially to attain the desire local girth. After combining all component codes to generate an expanded parity-check matrix, the resulting girth is greater than or at least equal to the highest girth of component codes. We investigate a lower bound for circulant permutation matrices in the proposed method, which provides efficient and fast encoding for a desired girth, and has very simple structure and more economical in terms of hardware implementation. As already proven, a high girth parameter of the parity-check matrix ensures a good error correcting performance. Thus, simulation results show that our proposed construction method of the parity-check matrix significantly outperforms the other well-known existing methods, has low error-floor, and can reduce encoding complexity for medium to large block-length QC-LDPC codes.