Research On Efficient Projection Algorithms Of ADMM Decoding For LDPC Codes

Low-Density Parity-Check(LDPC)codes are a class of linear block codes with good error-correcting performance,and the codes are widely used in various fields such as ground-to-air communication,storage coding,mobile communication,etc.With the arrival of the era of massive data,communication systems put forward higher requirements for the efficiency of data transmission.Therefore,it has become a research hotspot in academia to design decoding algorithms with good performance and reduced complexity.Belief Propagation(BP)decoding and Linear Programming(LP)decoding are two types of classical decoding algorithms for LDPC codes.Alternating Direction Method of Multipliers(ADMM)decoding,which was proposed in 2011,combines advantages of both BP decoding and LP decoding,and shows a promising prospect.The Euclidean projection algorithm,which is used to project a vector of real values onto the parity polytope,is the most complex operation in ADMM decoding.Therefore,it is of great significance for ADMM decoding to develop more efficient projection algorithms.Different kinds of Euclidean projection algorithms are investigated in the thesis,and the main contents are summarized as follows: 1.The digital communication system and three classical channel models are outlined.Then the related concepts of linear block codes and LDPC codes are overviewed.In addition,the error-correcting performances of three typical decoding algorithms for LDPC codes,including Sum-Product(SP)decoding,Min-Sum(MS)decoding and ADMM decoding,are analyzed in detail.2.The disadvantages of Iterative Euclidean Projection Algorithm(IEPA)are slow convergence speed and too many times of iterations.By introducing Binary Search(BS)algorithm into the iterative process,BS-based Iterative Euclidean Projection Algorithm(BS-IEPA)is proposed.Within the tolerance,simulation results show BS-IEPA needs fewer iterations than traditional IEPA and the average execution time for a single projection operation is reduced by about 15%.3.Existing projection algorithms involve either sorting operation or iterative process,which leads to higher computational complexity.By taking the even-vertex closest to the input vector as an approximation of exact projection result,Approximate Polytope Projection Algorithm(APPA)is proposed.Simulation results show compared with existing projection algorithms,the averge time for a single projection operation with APPA is shorter.According to simulation results of three typical LDPC codes,error-correcting performance loss of ADMM decoding with APPA does not exceed 0.5 dB.