Research And Improvement Of Decoding Algorithm Of Polar Codes

Polar codes is the first channel coding scheme that has been proved to reach Shannon's channel capacity by mathematical method.Once it is proposed,it has a great influence in the field of communications.Polar codes has been successfully included into the 5G standard as a coding scheme for control channels in the Enhanced Mobile Broadband?eMBB?scenarios.It is believed that the application prospect of polar codes will be excellent.In the practical application scenarios,there are still many problems to be solved in polar codes with a limited code lengths.Particularly,it is important to improve the decoding performance of the polar codes in medium and short code lengths.Therefore,this paper focuses on the research of successive cancellation list?SCL?decoding algorithm and the CRC-Aided SCL?CA-SCL?decoding algorithm of polar codes.Then it was found that the performance of the SCL decoding algorithm can be greatly improved by CRC assisted.Inspired by this idea,we considering use other excellent error detecting codes to assist the SCL decoding algorithm.Therefore,for the first time,this paper proposed using the Internet Checksum?ICS?,Fletcher Checksum?FCS?and Weighted Sum Codes?WSC?to assist the SCL decoding algorithm.Three improved decoding algorithms are proposed,which are ICS-Aided SCL?ICSA-SCL?decoding algorithm,FCS-Aided SCL?FCSA-SCL?decoding algorithm,and WSC-Aided SCL?WSCA-SCL?decoding algorithm.The simulation results show that the three improved decoding algorithms obtain a certain performance gain compared to the SCL decoding algorithm.When the frame error rate?FER?is1×10^-3,the length of polar code is 1024 and the code rate is 0.5,There are approximately 1.0dB performance gain under ICSA-SCL decoding algorithm and 0.9dB performance gain under FCSA-SCL decoding algorithm and 0.8dB performance gain was obtained under the WSCA-SCL decoding algorithm.Compared to CA-SCL decoding algorithm,ICS in the ICSA-SCL algorithm and FCS in the FCSA-SCL algorithm have lower computational complexity than CRC that in CA-SCL algorithm when generating same check sequences.Moreover,the FER performance of the ICSA-SCL decoding algorithm is as good as CA-SCL decoding algorithm at low SNR,the FER performance of FCSA-SCL decoding algorithm is as good as the performance of CA-SCL decoding algorithm when selected an appropriate length of check sequence.WSCA-SCL decoding algorithm has slightly improved performance at lower SNR than CA-SCL decoding algorithm when selected an appropriate length of check sequence.When the length of polar codes is 1024 and codes rate is 0.5,the FER of the WSCA-SCL decoding algorithm is2.25×10^-2,and the FER of the CA-SCL decoding algorithm is 3.5×10^-22 under 0.5 dB SNR.