Research On Strongly Coupled LDPC Convolutional Codes Based On Faster-than-nyquist System

High-speed data transmission and high spectral efficiency are important research directions in today's mobile communication technology research,the Faster-than-Nyquist(FTN)transmission technology can improve the spectral efficiency by compressing the transmission interval between adjacent pulses.Low density parity check convolutional code(LDPC-CC),as a codeword in the forward error correction(FEC),has the characteristics of approximating Maximum-a-Posteriori(MAP)decoding.Sliding window decoding scheme can utilize the semi-infinite convolution structure of LDPC-CC codes to implement the decoding of super long data,while maintaining the advantage of low complexity of the traditional LDPC block codes using belief propagation(BP)decoding.In this thesis,we will study the combination of the advantages of FTN technology and LDPC-CC codeword,and the research work and innovation are as follows:(1)Based on the characteristics of small matrix dimension and large syndrome former memory of periodic strongly coupled LDPC-CC,the matrix of periodic time-varying strongly coupled LDPC-CC is regrouped into a form similar to that of time-invariant weakly coupled LDPC-CC,and a simplified coding scheme of periodic strongly coupled LDPC-CC is proposed,which can synchronize the coding and sliding window decoding of LDPC-CC.In addition,because the systematical generator matrix is used for special submatrix,it is not necessary to inverse the full rank matrix,and two different sliding window decoding and updating methods in LDPC-CC are introduced.(2)Aiming at the construction and optimization of strongly coupled LDPC-CC codewords,this thesis proposes a complete scheme.Firstly,a base matrix with good girth characteristics is constructed based on the protograph.In this step,the original algorithm of constructing base protomatrix can only construct a protomatrix with a code rate of(n-l)/n,and this limitation will be removed in this thesis.The improved algorithm can construct a base protomatrix with a girth of 6 at any code rate,and the number of search states are reduced by three orders of magnitude,and the theoretical lower bound of the syndrome former memory of the base protomatrix under the condition of no 4-ring at any code rate is further given;secondly,the degree matrix is further optimized based on the given base protomatrix,so that the girth and ring characteristics of the codeword are as good as possible,and the minimum dimension size of LDPC-CC is given to count the girth and ring characteristics of LDPC-CC under any period.In Nyqusit transmission system,simulation results show that the regular LDPC-CC can achieve 0.13 to 0.54db gain compared with regular LDPC-BC at 2/5 to 4/5 code rate,and with the decrease of code rate,the relative gain is greater,which verifies the effectiveness of the LDPC-CC construction algorithm proposed in this thesis.(3)In FTN system model,LDPC-BC transmits information in block or frame mode,LDPC-CC can be regarded as the cascade of LDPC-BC.Because LDPC-CC can transmit information bits in infinite length,the sliding window mode that the equalization iterative system of FTN also adopts is proposed in this thesis,which is combined with the sliding window decoding used in LDPC-CC decoding,so that the two can match each other and it is not necessary to wait for receiving all the information of LDPC-CC to start the equalization decoding of FTN,thus the decoding delay can be redeuced.Furthermore,for the FTN system,the improved dichotomy protograph-extrinsic information transfer(P-EXIT)tool is used to obtain the convergence characteristics of the base protomatrix in the FTN system,and analyze the base protomatrix matched to the FTN system.In the FTN transmission system,taking 2/5 code rate as an example,according to the result of dichotomy P-EXIT analysis of the base protomatrix,the corresponding irregular LDPC-CC code is constructed.In FTN system,when the squizing factor is 0.91 and 0.8,the gain of the optimized LDPC-CC is 0.49dB and 0.56dB compared with LDPC-BC.respectively,and the spectral efficiency is 9.9%and 25%higher than that of the orthogonal system.