Research On Two Improved Decoding Algorithms Of Polar Codes

Polar coding is the first channel coding scheme which is proved theoretically to achieve the Shannon channel capacity.It has quickly become a research hotspot in the coding field with its low decoding complexity and superior performance.Since the polar coding has been selected as the short-code scheme for the control channel in the 5G standard,scholars are increasingly enthusiastic about the research of polar codes.The research on its decoding algorithms make contributions to the practical applications.Based on the existing decoding algorithms of polar codes,this paper analyzes and studies parallel decoding and serial decoding respectively,and proposes two improved polar codes decoding algorithms.The main work of this paper is as follows:?1?Firstly,we study and analyze the parallel decoding algorithm of polar codes,and an it-erative decoding algorithm based on adaptive check matrix is introduced.Then the internal iteration and termination strategy is added to the algorithm through feasibility analysis.Fi-nally,a Modified Adaptive Belief Propagation?MABP?decoding algorithm of polar codes is proposed.The simulation results show that the performance of the MABP decoding algo-rithm become better as the number of internal iterations increases,but considering the com-plexity problem,the value should be set reasonably.When the frame error rate is 1×10^-3,the MABP decoding algorithm with 50 internal iterations has a performance gain of 0.35 dB compared to the original BP decoding algorithm in the condition of code length of 1024 and code rate of 0.5,and this decoding algorithm has certain research value for the short code scheme of the polar codes in the 5G control channel.?2?Secondly,considering that the MABP decoding algorithm is a soft output decoding method and in order to further obtain a good compromise between complexity and per-formance.This paper also proposes two cascaded schemes with MABP decoding algorithm,namely Order Statistic Decoding?OSD?cascade MABP and Accumulated Log Likelihood Ratio?ALLR?cascade MABP.The simulation results show that the performance of OSD cascaded MABP decoding algorithm with 50 internal iterations approaches the decoding performance of SCL-CRC in the condition of code length of 1024 and code rate of 0.5,but at the expense of space complexity.The ALLR cascaded MABP decoding algorithm further reduces the decoding delay.?3?Finally,the serial decoding scheme of polar codes is studied.We mainly analyze and improve the Successive Cancelation?SC?decoding and Successive Cancellation List?SCL?decoding algorithm.Although SC decoding can achieve Shannon capacity,it retains one local optimal path.The improved SCL decoding performance is better,but there is the posibility of losing path.For this reason,this paper proposes the Extended Successive Can-cellation List?E-SCL?decoding algorithm,which ensures that the SC path will be included in the reserved path of SCL.The statistical results show that the SCL decoding has a higher probability of losing the SC path under low SNR conditions.Therefore,the performance of the improved E-SCL decoding algorithm is slightly better than the SCL decoding algorithm.As the SNR increases,Their performance is comparable and the frame error rate curves tend to coincide.