Research On The Key Problems Of Linear Programming Decoding

Low density parity check(LDPC)code is one of the most popular channel codes,which has become the focus and hotspot of many research in recent years.Compared with other channel coding,LDPC code has many advantages,such as: LDPC code parity check matrix is sparseness,so its coding complexity is lower.Decoding complexity is low and can be decoded in parallel.LDPC code has been applied to the next generation of broadband wireless communications,optical fiber communications and other fields.In this paper,the linear programming decoding of LDPC codes and the development of pseudocodewords are deeply studied.The main achievements are as follows:Firstly,the advantages and disadvantages of the iterative decoding algorithm of LDPC codes are studied,including BF decoding and BP decoding,and the influence of ring on the decoding performance in the parity check matrix is pointed out.Secondly,the paper introduced the mathematical model of linear programming and its application in mathematical problems.Then,the application of linear programming in error correction code and the process of relaxation of integer linear programming are given.Elaborated principle and process of Linear Programming Decoding.The simulation results of the original LP decoding application in the LDPC code are given.Compared the complexity and performance of the BP decoding by simulation results.Then,the concept of LP decoding maximum likelihood guarantee characteristic is given.Based on the simulation performance of the original LP decoding,the paper analysis the advantages and disadvantages of the original LP decoding,and the multystage linear programming(MLP)decoding is introduced on the basis of the original LP decoding principle.The principle and algorithm flow of multystage linear programming are described in detail.The paper analysis the decoding performance of multystage linear programming decoding and the relationship between decoding complexity and number of holes is analyzed.Based on the original LP decoding?MLP decoding and BP decoding,this paper proposes a mixed decoding method,which transforms the failed decoding sequence into soft information on the probability domain.In this paper,the soft information refers to the bit likelihood ratio.The LP or MLP decoder which decodes failed is regarded as a means for improving the confidence of the soft information,and then the soft information is input to the BP decoder for decoding.It can be seen from the simulation diagram that the mixed decoding simulation proposed in this paper is improved compared with MLP decoding,and the complexity is almost no increase.It is suitable for applications with high reliability requirements.Based on the improvement of the complexity index of MLP decoding,this paper proposes an adaptive MLP decoding method.The basic idea is to use the hierarchical idea of tree in the data structure to select the unreliable points to sort and decoding in level.One layer can end the decoding.The adaptive MLP decoding in this paper can be compromised in complexity and performance,and this adaptive decoding method is applied to mixed decoding to increase the flexibility.