By making the pseudocodewords more costly

the penalized decoding method based on alternating direction method of multipliers (ADMM) can improve the decoding performance for low-density parity-check (LDPC) codes at low signal-to-noise ratios and also has low decoding complexity.Reducing the number of Euclidean projection in ADMM penalized decoding

selecting the appropriate message scheduling strategy and designing effective penalty function are three important methods to increase the ADMM penalized decoding speed.In order to increase the ADMM penalized decoding speed further

by using

the method proposed by Wei et al to reduce the number of Euclidean projections

this paper designs two kinds of ADMM penalized decoding methods with the horizontal layered scheduling and the vertical layered scheduling strategy for LDPC codes based on the I-

l

1

-PF penalty function.Simulation results show that the designed methods not only have better decoding performance but also significantly reduce the average number of iterations and the average decoding time compared with the existing ADMM penalized decoding methods.