Bisection Method Assisted Affine Projection Algorithm in ADMM-LP Decoding of LDPC Codes

Many researchers have proposed optimization methods to reduce the computational complexity of the Euclidean projection onto check polytope in the alternating direction method of multipliers (ADMM) decoding for Low-Density Parity-Check (LDPC) codes. Existing the sparse affine projection algorithm (SAPA) projects the vector to be projected onto an χ-dimension affine hull and the dimension χ is fixed, resulting in deteriorating decoding performance. In this letter, bisection method assisted affine projection algorithm is proposed to determine the correct projection dimension for each the vector to be projected with the bisection method iterative algorithm. Simulation results show that the proposed algorithm can improve the accuracy of projection results by 68.2%. The FER performance of the proposed algorithm is almost the same as that of the exact projection algorithm, and compared with the sparse affine projection algorithm (SAPA), it can improve the FER performance by 0.14 dB as well as save average number of iterations by 3.2%.