Research On Polar Code Decoding Algorithm Based On SC

Polar code,a new type of channel coding,was proposed in 2009.Because it has been proved to be able to obtain the channel capacity,and has the advantages of low coding complexity and fixed encoding and decoding structure,it has extremely high research value.This paper first introduces the channel polarization theorem,and simulates the BEC polarization channel capacity distribution by using MATLAB to verify the correctness of the channel polarization theorem.After that,the greedy algorithm was used to find out the optimal signal-to-noise ratio points of the three coding construction methods in this paper at a given number of SNR points.Finally,polar code encoding is introduced.In the polar code decoding algorithm,this paper deeply researches the existing polar code decoding algorithms such as SC,SCL,CA-SCL,SFSC.The researches show that CA-SCL decoding algorithm has excellent performance,but its computational complexity is high and decoding delay is large.SFSC decoding algorithm has lower computational complexity in high signal-to-noise ratio environment,but its performance is not good.Aiming at the problem that the CA-SCL algorithm has high decoding complexity and large decoding delay at high SNR.In this paper,a Bit-Flipping-Based Successive Cancellation List（SFSCL）decoding algorithm is proposed based on bit flipping idea.In decoding performance,When the SC decoding fails,the SFSCL decoding algorithm starts to execute the CA-SCL decoding algorithm.When calculating the extended path metric at the position of the SC decoding error decision,the last extended path metric is subtracted from the product of a penalty factor and the absolute value of the log-likelihood ratio to indirectly implement bit flipping,so as to further improve the decoding performance of CA-SCL.The MATLAB simulation results show that the performance of the SFSCL decoding algorithm with a list width of 2 and bit flipping times of 8 is about 0.3 dB higher than that of the SFSC with the same number of bit flips at the error frame rate of10^-3.Compared to the CA-SCL with the same list width,the decoding algorithm has a performance gain of about 0.25 dB.In decoding complexity,the SFSCL decoding algorithm first performs SC decoding.Since the success rate of the SC decoding algorithm is gradually increased in the case of a high SNR,the probability of requiring additional bit-flipping operations is gradually reduced,thereby greatly reducing the average computational complexity of the SFSCL decoding algorithm under high signal-to-noise ratio conditions.The MATLAB simulation results show that the average complexity of the SFSCL decoding algorithm gradually converges to the complexity of the SC decoding algorithm as the signal-to-noise ratio increases.The average complexity of the SFSCL decoding algorithm with the list width of2 and the number of bit flipping 8 is reduced by approximately 50%compared to the CRC-SCL decoding algorithm with the same list width at the signal-to-noise ratio of 3.5dB.