Research On Algebraic Construction Of Quasi-cyclic LDPC Codes And Decoding Algorithm Of LDPC Codes

The low-density parity-check code was originally proposed by Dr. Gallager in 1962, which cannot attract a large amount of interest at that time. However, after decades of years, it is now rediscovered by Mackay and Neal, along with the enhancement of computer ability and the development of some related theories, such as graph theory, BP algorithm, turbo codes principle, etc. It is also shown that the performance of LDPC codes is very close to the Shannon limits with sufficient long block length when decode using the BP decoding algorithm.This paper researches an algebraic method of constructing LDPC codes .Firstly, it proposes a parameter selection method and gives a girth detection algorithm for the cyclical shift parameter matrix.Secondly,the paper analyses other two functions for constructing the cyclical shift parameter matrix.The paper considers the power function and the trigonometric function as the construction function of the cyclical shift parameter matrix.Then it gives the random construction method of the cyclical shift parameter matrix.Finally the paper analyses the performances of the LDPC codes mentioned above using computer simulation.This paper also researches three typical decoding algorithms that are bit flipping algorithm, belief propagation algorithm and LLR-BP algorithm.By simulation, the result proves that LLR-BP algorithm is the best one of them considering the balance between time complexity and perfomances of decoding.