Length-compatible PEG-CRT algorithm

Among the existing methods for the construction of random-like LDPC codes, one of the most successful approaches is progressive-edge-growth (PEG) algorithm. This approach is simple but the complexity of the PEG algorithm scale as O(nm), where n is the number of symbol nodes and m is the number of check nodes. The PEG-CRT algorithm deals with this problem by construct a base matrix H_b of size m_b × n_b with the PEG algorithm and expand this base matrix into a parity-check matrix H of size m × n via the chinese remainder theorem (CRT), where m >> m_b and n >> n_b. The size of the base matrix is expanded without decreasing the girth. Since a smaller matrix is constructed with the PEG algorithm and the complexity of the CRT computation is negligible compared to the PEG algorithm, the complexity of the whole code construction process is reduced. However, unlike the PEG LDPC codes, the code lengths of PEG-CRT LDPC codes are not flexible. To solve this problem, in this paper, we propose a length compatible PEG-CRT algorithm, which preserves good properties such as large girths, flexible code rates, flexible code length and low densities.