Research On Construction And Decoding Of Globally Coupled LDPC Codes

A globally coupled low density-parity check(GC-LDPC)code is a special class of low density-parity check(LDPC)codes whose parity-check matrix is composed of several local matrices and a globally coupled matrix.The structure of the GC-LDPC code is beneficial for the phase of local decoding and globally coupled decoding,so it greatly simplifies the complexity of the decoder.This paper focuses on the construction of GC-LDPC and the design of code decoder.We construct a parity-check matrix for achieving better performance and design a more efficient two-phase decoder.Firstly,since the t circulant matrices of(q,n,g,r,1)-BIBD satisfy the row column(RC),a new replacement set constructed by t circulant matrices can be used to contruct a BIBD-based GC-LDPC(BIBD-GC-LDPC)code.The simulation results show that the performance of this code is improved by at least 0.2 dB over the AWGN channel when BER=10-5,compared to that of GC-LDPC code based on the finite field(FF)replacement set.Secondly,we found that the performance of two-phase decoding algorithm has at least 0.5 dB gain loss compared to that of the sum-product algorithm(SPA)when BER=10-5.To solve this problem,we propose a two-phase alternative decoding algorithm.The algorithm adds a new decoding phase to feedback the information from the global coupling phase to the local decoding phase.The simulation results show that the alternating algorithm has at least 0.2 dB gain compared to the two-phase decoding algorithm when BER=10-6.At the same time,the computational cost can be reduced by 33%compared to the SPA.Furthermore,we propose a hybrid two-phase decoding algorithm.The algorithm sends the output of the global coupled decoder to the whole decoder for next decoding phase so that the code can be redecoded.The simulation results show that the hybrid algorithm has at least 0.35 dB gain compared to the two-phase decoding algorithm when BER=10-5.At the same time,the computational cost can be reduced by 32%compared to the SPA.Finally,we propose a non-sparse global coupling structure.This structure strengthens the link relation between the local matrices and the global coupling matrix and leads to two advantages:the improvement of code rate and the elimination of the effection of 4-cycle in the parity check matrix.The simulation results show that the performance of the two-phase alternating decoding algorithm can be improved by at least 0.5 dB compared to the SPA when BER=10-5.