Research On Efficient Encoding And Decoding Algorithms For Polar Codes

Polar code is a new developing error correcting code.This coding has received wide attention.Because it is the only coding which can be proved that the capacity is achievable.Although the-state-of-art channel coding methods of LDPC and Turbo can be very close to Shannon capacity in simulations,none of them can give strict proof in theory.The most prominent advantage of polar codes is that it can be encoded and decoded using simple encoders and decoders.Moreover,for a given code length N,the complexity of the implementation of the coding and decoding process is O(Nlog N).However,the decoding performance of polar codes is not satisfactory under medium or short code length conditions in practical communication systems.This thesis focuses mainly on the research of various polar decoding algorithms under the condition of medium or short length.The main research results include the following aspects: 1.This thesis firstly discusses the parity-check concatenated cyclic redundancy check(CRC)aided successive cancellation list(CA-SCL)decoding algorithm,and proposes a new double parity-check CA-SCL decoding method.The proposed algorithm can effectively improve the block error rate performance of polar codes under the medium or short code length condition.Secondly,this thesis also chooses Hash concatenated polar codes as the research object,and changes the original structure of Hash concatenated polar codes taking the distributed CRC polar codes as inspiration,.The distributed Hash-Polar scheme can further improve the error performance.2.Soft output cancellation(SCAN)decoding algorithm is based on the iterative decoding algorithm.Considering many complex formula operations in the decoding process,this thesis revises the decoding algorithm and proposes an improved SCAN decoding method.Using the idea of function segmentation and function approximation,the node update formula is simplified,which greatly reduces the complexity of SCAN iterative decoding process,and ensures that the error rate performance of the improved algorithm is no loss compared with the original soft cancellation decoding.3.SCAN is a practical algorithm that can provide soft output.However,the performance of iteration-based decoding still lags the CA-SCL decoding.Enlightened by the SC-Flip decoding algorithm,this thesis proposes a SCAN-Flip method based on likelihood.By adjusting the logarithm likelihood information of the iterative decoding process,SCAN-Flip method can correct decoding errors and improve the performance to a certain extent.4.Due to the encoding characteristics of polar codes,the code length of polar codes is limited to the power of 2.The puncturing technique is one of the key methods to solve the code length compatibility problem.Aiming at the special requirement of codeword length in satellite navigation system,this thesis combines the existing non-system polar code's puncturing methods,and demonstrates the expansibility of puncturing method in systematic polar code.A simple puncturing technology based on the recursive realization of polarization weight is proposed.The simulation results show that the performance loss of the new puncturing method is smaller than that of the existing methods.