Research On Encoding And Decoding Algorithms Of Polar Codes

Polar codes are error-correcting codes that has been proved to reach Shannon limit.Compared with Low-Density Parity-Check Code(LDPC)codes and Turbo codes,they have lower computational complexity and better encoding and decoding performance.Since 2008,it was first proposed by Professor Erdal Arikan of Turkey's Biken university that the performance of linear encoding and decoding of polar codes has attracted the attention of many experts in the field of channel coding.Currently,the polar codes has been determined as the control channel encoding scheme for mobile broadband scenarios in the advancing 5G communication standard.It is believed that the polar codes will be applied to a wider range of fields in the future.The construction of polar codes is based on channel polarization,and its encoding and decoding algorithm is also two different steps for channel polarization correspondingly.In 2011,Systematic Polar Codes(SPC)proposed by Arikan has lower bit error rate compared with Non-Systematic Polar Codes(NSPC)under the same modulation mode and channel condition.In this paper,we proposed an optimized encoding algorithm(OEA)which can reduce the number of XOR computing units according to the iterative property of the generator matrix and special lower triangular structure of the matrix.The OEA is optimized from the point of view of generator matrix.And it is proved that this property of the generator matrix can be extended to any code length and any rate of the polar codes.Through the matrix segmentation and transformation,we obtain a sub-matrix with all zeros to save computation resource.Compared withO(N~3)reported in the literature,the computing complexity of our OEA can be reduced toO(N~2),and it will not affect the frame error rate and bit error rate.The percentage of zero elements in the matrix can reach up to 58.5%for SPC when code length is 2048 and code rate is 0.5.It has been shown that the half the computing resources can be saved for our optimized encoding algorithm in future hardware implementation.At present,the decoding algorithms of polar codes are mainly Successive Cancellation(SC)decoding algorithm and Belief Propagation(BP)decoding algorithm.Based on the SC algorithm,the different code lengths of different code rates are simulated respectively.The simulation results show that when the code length is longer and the bit rate is lower,the bit error rate is lower,and the decoding performance of polar codes is better.Taking N(28)8 as an example,the computing characteristics of SC decoding algorithm in each clock cycle and the type of computing unit used in each clock cycle are studied in this paper.This paper proposes a low latency and low complexity Simplified Successive Cancellation List(S-SCL)decoding algorithm which is based on the research of Simplified Successive Cancellation(SSC)algorithm and Successive Cancellation List(SCL)algorithm.It is proved that the S-SCL algorithm not only has the low computation time delay of the SSC algorithm,but also has the better decoding performance of the SCL algorithm theoretically.Finally,the research on the feasibility of the polar codes,LDPC code and Turbo code multi-mode decoder is presented.