Investigations On The Construction And Decoding Of Low-Density Parity-Check Codes

Low-Density Parity-Check(LDPC)Codes is an outstanding channel coding scheme which has been proven to approach Shannon limit.Due to their powerful decoding performance,LDPC codes gained considerable research attention in recent years.In 1963,LDPC codes together with its two basic decoding algorithms,which are called Bit Flipping(BF)algorithm and SumProduct Algorithm(SPA),were proposed by Gallager in his doctoral thesis.The BF decoding algorithm has low complexity and medium bit error rate(BER)performance,while the SPA decoding algorithm has high complexity and excellent BER performance.In order to shorten the gap between the two decoding algorithms and provide more trade-offs between complexity and BER performance,many variants of these two decoding algorithms have been proposed.To help the Single Noisy Gradient Descent Bit Flipping(S-NGDBF)decoding algorithm escape from the local maxima,we propose the Single Tabu-List Noisy Gradient Descent Bit Flipping(S-TNGDBF)decoding algorithm.The S-TNGDBF decoding algorithm uses a tabulist to prevent the same bit to be flipped at any two successive iterations.Simulation results show that adding one tabu-list can enhance the ability of making the decoder escape from the local maxima and improve the BER performance.Then,we study whether adding more tabulists and using re-decoding can further improve the BER performance,and prove the feasibility through simulation.To reduce the waste of time and computing resources of failure decoding of Multi Noisy Gradient Descent Bit Flipping(M-NGDBF)decoding algorithm,we propose an early stopping criterion for M-NGDBF decoding algorithm in absence of an external Signal-to-Noise Ratio(SNR)estimator.The proposed early stopping criterion is based on the number of flipped bits at some specific iterations,and has extremely low complexity.Simulation results show that the proposed early stopping criterion can significantly reduce the average number of decoding iterations at low SNRs,and only a slight BER performance loss is experienced at high SNRs.