Research And Design Of Rate-compatible Multivariate LDPC Code

Rate-compatible non-binary low-density parity-check codes（RC-NB-LDPC）is an indispensable part of wireless communication systems that can dynamically adapt to channel changes and improve power and spectrum resource utilisation while ensuring reliability.Puncturing is one of the effective ways to achieve low to high code rate transition in rate-compatible technologies,but removing the check information will result in partial loss of decoding information and degrade decoding performance.Firstly,to reduce the impact of puncturing on decoding performance,two cycle-based puncturing algorithms for non-binary LDPC codes are proposed.The bitwise puncturing algorithm extends the non-binary check matrix to the binary domain and gives preference to bits which contain large cycle for puncturing.The symbolwise puncturing algorithm redefines cycle of symbols,uses the maximum cycle of bits as cycle of the corresponding symbols,while selecting the large cycle symbols for puncturing.The simulation results show that both cycle-based puncturing algorithms have some improvement in decoding performance compared with the random bitwise puncturing algorithm.Secondly,to improve the probability of correct recovery of lost decoded information,a recovery-tree-based bitwise and symbolwise puncturing algorithms for non-binary LDPC codes is proposed.The bitwise puncturing algorithm gives preference to bits with a low number of iterations for puncturing.Symbolwise puncturing is divided into two algorithms:grouping and sorting.The grouping algorithm defines the maximum number of iterations of bits as the number of iterations k of the corresponding symbols,and groups the symbols into sets G_s=(G_s1,G _s2,（43）,G_sk)based on k.The sorting algorithm sorts the bits of symbols in the grouped set according to the number of iterations.The lower the number of bit iterations,the higher the probability that the information of the corresponding symbols is correctly recovered.Simulation results show that the performance of the recovery tree-based bit-level punching algorithm is better than that of the random bit-level punching algorithm.The decoding performance of the symbol-level punching algorithm based on the recovery tree not only surpasses that of the random bitwise puncturing algorithm,but also significantly outperforms the traditional puncturing scheme and the proposed other improved algorithms,making it an efficient and reliable rate compatible algorithm.