Algorithms And Implementations For Polar Codes

In the key technologies of 5G,efficient channel coding and decoding scheme has become to an important research direction.Among them,LDPC code is adopted as the data channel long code block coding scheme under the 5G eMBB scenario,and Polar code is adopted as a short code scheme in 5G control channel.This paper mainly focus on these two kinds of channel codes,POLAR codes and LDPC codes.Different algorithm and architecture of the two codes are proposed in this paper.In this paper,a polar code encoding and decoding platform based on SCL decoder is pro-posed.The innovative distributed sorting algorithm and efficient folding decoding scheme are provided in the platform.To deal with the large complexity and long latency of SCL sorting,an innovative distributed sorting algorithm is proposed.This sorting algorithm is a low complexity sorting algorithm by using SCL decoding characteristics.When the length of the list is L,the complexity of the distributed sorting algorithm is reduced from O?L²?to O?L?,and the sorting latency is reduced from L²to L.According to the simulation results,we can see that the in-fluence of distributed sorting algorithm and strict sorting algorithm on the performance of SCL decoding is negligible.In view of the huge consumption of polar code hardware architecture,this paper proposed a SC folding architecture based on k-level decomposition.The essence of the idea is to divide the original n-level decoding architecture into two parts by introduc-ing the principle of polar code decomposition,and introduce parallel factor p.The folding and pipelining operation of the secondary decoder greatly reduce the hardware complexity of the decoder and improve the utilization ratio of hardware resources.If the folding operation is ex-tended further and the original two segments extended to multistage folding,the advantages of the utilization of the hardware resources will be further expanded.This paper proposed a SC folding architecture based on k-segment decomposition.We built a complete polar code encoding and decoding platform based on the innovative decoder scheme and sorting scheme,and implemented it on Stratix V.And put forward some suggestions for the improvement of the platform.Three frames of L parallel SC decoding and SCL decoding,adaptive SC and serial SCL decoding,adaptive deep pipelined SC and SCL joint decoding are proposed as well.In addition to implement the basic SCL coding and decoding platform,this paper further discusses the enhancement of decoding performance,efficiency and complexity of the efficient algorithm structure for the poled code decoding algorithm.This paper proposed an efficient polar code decoder based on heap SC algorithm.The main idea is to decode along the path of maximum metric value,and to press the metric as a heap,and continuously extract the path with the maximum path measured by the efficient heap sort.By introducing node deletion,the decoding efficiency is improved.Simulation results confirm the corresponding relationship between L=Q/2 performance?the correspondence between SCL settings and SC decoding settings on unified performance?.Through the analysis of the average link length,it is found that the SC decoding length based on the heap under?D=2⁹-1,Q=8?saves 63.53%compared to the average decoding length of SCL under the same decoding performance.This paper also gives a detailed decoding architecture and hardware implementation scheme for the proposed heap SC decoding algorithm.And tree search method is proposed to reduce large area storage space.In order to solve the problem of decoding complexity and decoding redundancy,this paper proposed a SCL decoding algorithm based on segemented CRC?SCA-SCL?.Compared with CA-SCL,segmented verification improves the decoding efficiency and reduces the storage area.This paper also discusses how to optimize the allocation of each segment of the CRC,starting with the requirements of the segment,defining the new virtual transmission and virtual length to get the best way of CRC matching.Compared to the performance of the SCL decoding algorithm with an average allocation of CRC,the proposed TCA-SCL decoding algorithm has a 0.1dB performance gain in a place where the frame error rate is FER=10^-2.This paper proposes a BCH-CRC based SCL polarization code decoding algorithm?BC-SCL?,and gives an improved version of HARQ.The scheme is based on a modified version of the segmented CRC decoding scheme.Compared with the traditional piecewise CRC decoding algorithm,the BC-SCL algorithm proposed in this paper has 0.1dB performance gain at the frame rate of 0.1.Compared with the traditional piecewise CRC polar decoding algorithm,the HARQ BC-SCL?T=2?algorithm proposed in this section has 0.8dB performance gain at the frame rate of0.1.In this paper,the design of BC-SCL hardware decoding is also given.In this paper,we proposed a joint path extension decoding algorithm based on SC and SD.The performance of JLSCD is between SCL and LSD.Compared with SD performance,its frame error rate at 0.01 is only less than that of 0.1dB.A SCL decoding algorithm based on stochastic stream is proposed in this paper.The design uses the advantages of binary stochastic data stream decoding.The SCL decoder of random sequence is expected to be a good decoder with good performance,low complexity and strong fault tolerance.In order to improve the decoding performance,this paper introduces the doubling probability method and its approximate form.The corresponding hardware structure is also presented,which has advantages in performance and complexity.Other efficient channel codec algorithms are also discussed,involving LDPC codes,TBCC codes and so on.Tthis paper discusses the BP decoding method of LDPC codes based on non binary system.The performance and advantages and disadvantages of different path search methods are discussed in detail.In this paper,the NB-BP algorithm is further applied to the decoding of ordinary binary code,and the mapping relationship between the ordinary binary code and the non binary code is established,and the general NB-BP is used to decode the code.This operation extends the BP decoding from LDPC to the convolutional code such as TBCC,and uses a unified universal NB-BP decoder to ensure the decoding of various codes on the basis of its performance to a certain extent.MCMC algorithm is also discussed in this paper.First,the application of MCMC algorithm in MIMO detection is studied in general,and the problem of improving the performance fading of high signal to noise ratio detection is discussed.On this basis,the MCMC algorithm is transplanted to LDPC decoding,and the lifting method discussed in MIMO detection has been used to improve the performance of MCMC in codec to some extent.A preliminary conclusion that MCMC algorithm is suitable for short code is not suitable for long code is given.