Research On ADMM Decoding Scheduling Algorithm Based On Approximate Projection

Due to the advantages of excellent performance,infinitely close to Shannon limit,and simple encoding,Low Density Parity Check(LDPC)codes have been studied by many coding and decoding scholars.At the same time,LDPC code decoding algorithms with different characteristics have been proposed one after another.Among them,the Linear Programming(LP)decoding algorithm based on the Alternating Direction Method of Multiplier(ADMM)has attracted wide attention for its advantages such as all-zeros assumption and maximum-likelihood(ML)certification property.The research on the ADMM-LP decoding algorithm mainly focuses on the following three aspects:1.Improve the decoding performance of ADMM-LP decoding algorithm.In this field,researchers have mainly enhanced the decoding performance of the ADMM-LP decoding algorithm in the low signal-to-noise ratio area by adding different penalty items to the objective function.2.Reduce the complexity of the ADMM-LP decoding algorithm.Since the Euclidean projection onto check polytope is the most complicated and time-consuming operation of the entire ADMM-LP decoding algorithm,a large number of scholars have proposed different simplified projection algorithms,such as cut search projection algorithm,approximate hybrid projection algorithm,approximate line segment projection algorithm,etc.3.Speed up the decoding speed of ADMM-LP decoding algorithm.Choosing an appropriate message scheduling algorithm can improve the speed of the BP decoding algorithm.Based on this strategy,scheduling algorithms suitable for ADMM-LP decoding have been successively proposed by researchers,such as horizontal layered scheduling,vertical layered scheduling and node-wise scheduling algorithm.Inspired by the above methods,this paper launched the following research work:1.An ADMM horizontal layered scheduling algorithm based on approximate projection is proposed.By analyzing the respective characteristics of the line segment projection algorithm,the hybrid projection algorithm and the horizontal layered scheduling algorithm,and combining the advantages of each algorithm,the approximate projection algorithms are applied to the horizontal layered scheduling algorithm.According to the simulation results,compared with the original algorithm,the proposed algorithms can not only greatly improve the decoding performance,but also have lower decoding complexity.In particular,the decoding performance can be improved by 0.1-0.4dB,and the decoding rate can be increased by about 5%-30%.2.Propose an ADMM node-wise scheduling algorithm with line segment projection.Based on the idea of combining the approximate projection algorithms and the scheduling algorithm,this paper uses the approximate line segment projection algorithm to perform the projection operation in the node-wise scheduling algorithm.It is verified by experiments that the direct use of approximate line segment projection instead of precise projection in the node-wise scheduling algorithm will deteriorate the decoding performance.To solve this problem,the reasons are analyzed and the residual calculation is improved in this paper,so that the line segment projection is suitable for the ADMM node-wise scheduling algorithm.Experimental results show that compared with other algorithms,the improved algorithm achieves 25%decoding speed improvement,a significant increase in decoding performance of 0.1-0.5dB and a significant savings in decoding time ranging from 20%-66%.In addition,combining it with the reduced-complexity node-wise scheduling algorithm can further accelerate the decoding speed of the algorithm while maintaining the decoding performance.