A Reduced-Complexity ADMM Based Decoding Algorithm for LDPC Codes

Alternating Direction Method of Multipliers (ADM-M) is an effective method for Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes. In the ADMM-based LDPC decoding algorithm, Euclidean projection on the check polytope is the key step. Current Euclidean projection algorithms in general require either sorting or iterative operations. However, when decoding LDPC codes with high coding rate, the sorting operation brings a high level of computation complexity. Moreover, although the current iterative projection algorithms do not involve the complex operation of sorting, its convergence speed is slow. In this paper, based on trend extrapolation, a reduced-complexity iterative check polytope projection algorithm is proposed. In the proposed algorithm, the target projection point can be found based on the variation trend of the geometric position of the projection points obtained from previous iterations. Therefore, it ensures fast convergence and does not sacrifice on bit error rate (BER) performance. The simulation results confirm that the proposed algorithm can effectively reduce the decoding complexity, especially for LDPC codes with high coding rate.