Research And Improvement Of Decoding Algorithm Of Polar Codes

Polar codes was a new channel coding scheme proposed by E.Arikan based on the channel polarization phenomenon in 2009.Polar codes are the first and currently,the only family of codes with explicit construction to achieve the Shannon's capacity of a certain family of channels as the block length goes to infinity proved by strict mathematical methods.They have encoding and decoding algorithms with very low complexity.Polar codes have been successfully included into the 5G standard as coding scheme for control channels in the Enhanced Mobile Broadband(eMBB)in 2016.It is believed that the application prospect of polar codes will be broad and excellent.Successive cancellation(SC)decoding algorithm is the first decoding method of Polar codes introduced by E.Arikan,which can be proved that the Polar codes achieve the Shannon's limit as the block length goes to infinity.However,at moderate block lengths,the performance of SC decoding algorithm is not perfect,which prevents them from being implemented in practice.Successive cancellation list(SCL)decoding algorithm and CRC-Aided successive cancellation list(CA-SCL)decoding algorithm are proposed to improve the performance of SC decoding algorithm.It is proved that the performance of SCL decoding algorithm can be improved significantly with CRC assisted which is usually used for channel error detection.We consider improve the performance of SCL decoding algorithm combined with Weighted Sum Codes(WSC)which have excellent capacity of error detection.In this paper,we aim at providing a scheme named WSC-Aided successive cancellation list(WA-SCL)algorithm to combine SCL algorithm with WSC algorithm.The new decoding algorithm check channels partially based on measures of channel reliability to get rid of the fewer maximum number of message bits protected of WSC.We introduce WA-SCL decoding algorithm by detailed description and algorithm flow chart.We notice that weighted sum codes are RS codes and it can be advantageous to use these codes for error correction in some cases.Inspired by this idea and concatenated codes,we consider taking advantage of the capacity of error correction of WSC to improve the performance of polar codes.A scheme for concatenating the polar codes with interleaved weighted sum codes is considered.By concatenating binary polar codes with interleaved weighted sum codes,we prove that the proposed concatenation scheme captures the capacity-achieving property of polar codes,while having a significantly better error-decay rate.At last,the simulation results confirmed our speculation about the performance ofWA-SCL decoding algorithm authentically.When the frame error rate(FER)is 1 × 10-3,the polar codes,whose length of codes is 1024 and code rate is 0.5,obtain approximately 0.6dB performance gain compared to SCL decoding algorithm with 12-bits check length.WA-SCL decoding algorithm obtains almost the same performance at lower SNR and a more excellent performance at higher SNR compared to CA-SCL decoding algorithm.When the SNR is 2.8dB,the performance of WA-SCL decoding algorithm begins exceeding CA-SCL decoding algorithm.Moreover,weighted sum codes combine the error detection properties of CRC with either efficient software and hardware implementations or commutative processing,and weighted sum codes have particular error correction performance which is CRC deficiency.The WA-SCL decoding algorithm and the WSC-polar concatenated code proposed in this paper achieve the results expected in simulation.