Low complexity encoding of LDPC codes for high-rate and high-speed communication

One of the weak points for LDPC encoding is the computational complexity in communication system. An efficient encoding was presented by Richardson who approached making codeword by using parity check matrices with low density. In this paper, we focus on computational complexity of Richardson´s LDPC matrix which is composed by matrix A, B, C, D, E and T. We propose two schemes for low complexity encoding. First one accomplishes T^-1 = E = I and restricts D consisting of dual diagonal matrices and second one achieves T^-1 = phi^-1 = I. Therefore the constraint reduces complexity from O(n+g²) to O(n) and efficiently omits some process of encoding. Also, we perform numerical experiments on our matrices. Proposed schemes can be useful for high-rate and high-speed communication systems due to reduced complexity and retrenched processes of encoding.