Research On Quasi-cyclic Low Density Parity Check Codes Based On Faster-than-nyquist System

In order to provide users with more diversified services and more smooth communication experience,the current communication systems urgently need to improve transmission efficiency and transmission reliability.Limited by the spectrum resources,the communication systems need to overcome the interference and noise in the channel by minimizing the power within a limited bandwidth.Faster than Nyquist sampling(FTN)technology can effectively improve the spectrum utilization of the system,so it has a great prospect of application.Low density parity check code(LDPC)has become a common channel coding method because of its very close-to-Shannon limit performance,which can effectively improve the reliability of communication system.LDPC convolutional codes can be regarded as the promotion of LDPC codes,which has become a strong competitor of LDPC codes with the advantages of simple encoding,better performance and flexible code length.In this paper,FTN technology and LDPC coding are used to build communication system,and the optimization method of LDPC codeword under FTN system is deeply studied,and further extended to the optimization of LDPC convolutional code under FTN system.This paper briefly introduces the basic principle of FTN technology and the system model of FTN system.On this basis,the three-wave model is introduced to further consider the interference between adjacent carriers.Then,the principle of LDPC code and LDPC convolutional code are introduced.And the key optimization index such as girth and ring characteristics of codeword are introduced to guide the evaluation of codeword performance.For the FTN system,a complete LDPC codeword optimization strategy is proposed in this paper,which consists of three parts,respectively,the optimization of the degree distribution,the optimization of the base matrix and the optimization of the degree matrix.The key idea is to find the best distribution of the check matrix for the FTN system with specific parameters and to optimize the base matrix and the degree matrix as much as possible to get a better check matrix girth and circle characteristics.Considering the close relationship between LDPC convolutional codes and LDPC codes,this paper introduces LDPC convolutional codes into FTN system and further extends the optimization algorithm to the construction optimization of LDPC convolutional codes.The simulation verifies the usefulness of the LDPC codeword optimization algorithm.Under the 1/2 rate single-wave model,the irregular quasi cyclic LDPC code optimized for FTN system achieves about 1.5dB gain compared with regular quasi cyclic LDPC code in FTN system.The LDPC CC codeword optimized for FTN system achieves an extra 1.5dB of gain,and the error floor of the codeword is even lower.Under the 7/8 rate three-wave model,the irregular quasi cyclic LDPC code optimized for FTN system achieves about 0.4dB gain compared with regular quasi cyclic LDPC code in FTN system.