Improved Belief Propagation Decoding Of Polar Codes

Polar coding was proposed by Ar?kan in 2009.It has been proved that this scheme is able to achieve Shannon limit.Consequently,more and more scholars have paid much attention to polar codes.The related research results have been put forward successively,which laid the foundation for application in a real scenario.In the 3GPP conference held in 2016,the polar codes were officially applied to the coding scheme of the control channel in enhanced mobile broadband scenarios in the 5G standard.The basic concept of polar codes and channel polarization are presented,respectively.The paper introduces the Successive Cancellation?SC?decoding algorithm and its improved Successive Cancellation List?SCL?decoding algorithm.These algorithms are running by successive processing.As a result,the corresponding delay is relatively high.The parallel decoding such as Belief Propagation?BP?decoding algorithm is studied.Compared with SC decoding algorithm,BP decoding algorithm has the characteristics of low latency and low bit error rate under the same conditions.Unfortunately,the complexity will increases with multiple iterations.Therefore,it is worthwhile improving this decoding algorithm.To begin with,original BP decoding algorithm was analysed theoretically.Belief Propaga-tion based on Likelihood Rate?BP-LLR?decoding algorithm and Belief Propagation based on stopping set?BP-LLR?decoding algorithm are proposed,respectively.These two algo-rithms adopt the unreliability of the point with the largest variance of the||value and the influence degree of point containing the most stopping set to correction.The bit which occurs error with high probability will be flipped.The simulation experiments of two algo-rithms are carried out with code length 2048 and code rate 0.5.Compared to the original BP decoding algorithm,BP-LLR decoding algorithm and BP-IC decoding algorithm have has a gain of 0.35dB and 0.1dB respectively when=6 and=10 with the frame error rate is 10^-3.Furthermore,BP-SS decoding algorithm and BP-IC decoding algorithm have has a gain of 0.45dB and 0.1dB respectively when=6 and=10 with the frame error rate is 6×10^-4.The average iteration number is regarded as decoding time complexity.The simulation results illustrate that average number of iteration is only about 2%higher than that of the original BP decoding.In order to improve the original BP-IC decoding algorithm,BP-ICSS decoding algorithm based on the stopping set is introduced since some flip is not necessary.This algorithm reduce the decoding delay.The simulation results show that average number of iterations of BP-ICSS is only 24%of that the original BP decoding algorithm and is about 10.3%lower than that of the BP-IC decoding algorithm.Another compromised BP-ICSS decoding algorithm presented in this paper reduces the number of CRC check.It is able to reduce the CRC check times by 89.8%when the decoding performance is close to the original BP-ICSS decoding algorithm.