Improved Belief Propagation Decoding Of Polar Codes

Polar code was proposed by Arikan based on the channel polarization phenomenon in 2009.It is a linear block code that can theoretically approach the capacity limit of Shannon's channel with low complexity.In 2016,3GPP decided to use the polar code as coding scheme for control channels in enhanced mobile broadband scenarios in 5G.And now,polar code has attracted a great attention in the field of wireless communications.At first,this article elaborated on the basic concepts of polarization phenomena which including channel combining and channel splitting.Then it introduced the encoding,construction and decoding methods of polar codes in detail.Among them,we emphasis the performance of polar code and the decoding algorithm,which including Successive-Cancellation decoding and belief-propagation decoding algorithms.This paper focuses on the belief-propagation decoding algorithm.In this paper,after a hard working on research and analysis of the original belief-propagation decoding algorithms,A modified belief propagation(BP)decoder of polar codes is proposed,which called Belief Propagation-Information Correction(BP-IC)decoding algorithm.There are two kinds of information correction strategies which including Flipped-Information-Correction strategy and Heuristic-Information-Correction strategy.Both strategies make a great improvement on the decoding performance of BP decoding.The simulation results show that in the condition of code length of 1024 and code rate of 0.5,compared with the original BP decoding,a gain of 0.75 d B was obtained with the BP-IC decoding based on Flipped-Information-Correction strategy.A gain of 0.9d B was obtained with the BP-IC decoding based on Heuristic-Information-Correction strategy.The two improved strategies increase the decoding performance,but they also bring the sacrifice on complexity.The simulation results show that compared with the original BP algorithm,the modified algorithms have higher complexity.But the average complexity of the two improved algorithms will come down when the noise ratio is decrease.We assumed that the iteration number of original BP decoding is 60.Then the average number of iterations of the BP-IC algorithm based on the Flip-Information-Correction strategy is 99.5 when the SNR is 2.75 d B.And the same value of the BP-IC algorithm based on the Heuristic-Information-Correction strategy is 92.When the SNR is 3.0 d B,the average number of iterations of BP-IC based on Flip-Information-Correction strategy is only 65,and the average number of iterations of BP-IC algorithm based on the Heuristic-Information-Correction strategy is only 69.At the last part of the paper,the early-stopping strategy with CRC is proposed to solve the problem of high complexity of the two improved decoding algorithms at low SNR.The simulation results show that the average number of iterations is reduced with a proportion more than 60%.