Research On Euclidean Projection Algorithm In ADMM Decoding

Low-Density-Parity-Check(LDPC) code has many advantages, such as simple structure, low decoding complexity, and performance closing to the Shannon limit, which makes it become a hot research. The Linear Programming(LP) decoding algorithm based on the Alternating Direction Method of Multiplier(ADMM) not only reduces the complexity of LP decoding, but also preserves the maximum likelihood certificate of LP decoding and the advantages of easy analysis in decoding LDPC codes.In the ADMM decoding algorithm, the key content is the Euclidean projection algorithm. The projection algorithm based on the cutting algorithm can greatly reduce the computational complexity and obtain better performance. However, the time complexity of decoding is still very high, and it is not suitable for large scale codes. In order to improve the decoding speed, a new projection algorithm based on simplex is proposed and studie d in detail. The main works of this paper are summarized as follows:1. Firstly, some basic properties about linear block codes and LDPC codes are briefly introduced, and Check matrix and representation method of Tanner graph about LDPC codes are given. Then sum product decoding algorithm and the maximum likelihood decoding algorithm of LDPC codes are described. Lastly, the decoding algorithm of LDPC codes based on linear programming is described seriously.2. The ADMM decoding algorithm theory of LDPC codes is analyzed, in which the projection algorithm based on cut search Euclidean projection algorithm is analyzed in detail, finally the ADMM decoding algorithm is simulated. The simulation results show that the ADMM decoding algorithm has better decoding performance and the decoding speed is better than that of the BP decoding and the min sum decoding.3. The projection algorithm in ADMM decoding is improved and a new projection algorithm based on simplex is proposed, and the projection of the simplex region in the algorithm is analyzed, lastly projection algorithm based on simplex is simulated. The results show that the decoding complexity based on the simplex projection algorithm is linear and the decoding time is shorter than that of the projection algorithm based on the cut search algorithm.