Research On The Construction Methods Of Rate Compatible QC-LDPC Codes

Low density parity check(LDPC)codes are a kind of forward error correction codes with excellent performance.However,in the complex environment,the simple code construction can not meet the needs of communication.Most channels in the actual communication system have some variability.Only one rate is used to transmit information can not take into account the effectiveness and reliability of the system.Rate compatible(RC)-LDPC codes are a group of LDPC codes with multiple code rates but the length of information bits unchanged.According to different channel environments,the code rate can be switched in time and no additional encoder and decoder will be occupied.This thesis mainly studies the construction method of rate compatible quasi-cyclic(QC)LDPC codes,and the research contents can be summarized as follows:1.Aiming at the high coding complexity of the current rate-compatible LDPC codes,the F-RC-QC-LDPC codes construction method based on matrix expansion and the Fibonacci sequence is proposed.The parity check matrix of the codes is divided into four parts: parent code matrix,zero matrix,sparse matrix and extended square matrix.The mother code matrix and extended square matrix are constructed based on Fibonacci sequence,while the sparse matrix has a fixed structure.The code length and code rate can be flexibly changed by setting the related parameters.The F-RC-QC-LDPC code with an information length of 2340 and a code rate set of {2/3,3/5,6/11,1/2,6/13} is constructed by this method.The performance of the F-RC-QC-LDPC code is very stable under the five code rates.Compared with the PEG-LDPC code constructed by the progressive edge growth(PEG),the multi-rate P-DY-QC-LDPC code constructed by Dayan sequence(DY)and the protograph,the DY-QC-LDPC code constructed by the Dayan sequence and the LS-QC-LDPC code constructed by Lucas sequence(LS),the net coding gain(NCG)of the F-RC-QC-LDPC code has been improved.2.Aiming at the problem of poor error correction performance of rate compatible LDPC codes constructed by puncturing,the P-RC-QC-LDPC codes construction method based on the protograph is proposed.The protograph extrinsic information transfer(PEXIT)algorithm is used to calculate the decoding threshold of the protograph for designing the base matrix of the protograph,and then the rate of the protograph is reduced by adding rows and columns.The protograph is expanded into a check matrix through two layers.By searching the best column vector on the shift coefficient matrix without four loops,the cyclic permutation matrix of the first layer is obtained,and then the cyclic permutation matrix of the second layer is selected by detecting six loops.Finally,the P-RC-QC-LDPC code with the girth of 8,the information length of 1228,and the code rate set of{2/3,4/7,1/2,4/9,2/5} is constructed.Compared with F-RC-QC-LDPC code,the error correction performance of the P-RC-QC-LDPC code is improved,but its storage complexity is higher than that of F-RC-QC-LDPC code.Under the approximate code length,the performance of P-RC-QC-LDPC code is better than that of RC-LDPC code based on algebraic theory,and the NCG of P-RC-QC-LDPC code is significantly improved when the code rates are 2/3,1/2 and 2/5.