Design Of Rate Compatible Polar Codes

Polar codes have received widespread attention since they were proposed.The polar codes use the polarization phenomenon generated by channel combination and splitting to perform coding design.Polar codes send information on good channels and fixed bits on bad channels.And it is currently the only code that has been proven to reach Shannon's limit.Polar codes' simple encoding method and low decoding complexity all highlight its infinite potential.It is possible that polar codes become another mainstream channel coding in the future.Due to the unique encoding method of the polar code,the reliability of the channel needs to be calculated to distinguish whether the channel transmits information or fixed bits.Therefore,a good channel reliability measurement method is very crucial.This paper introduces several reliability measurement methods.After analyzing and comparing their effects and implementation difficulties,we finally choose the Gaussian approximation method as the most suitable solution for the simulation environment of this paper.After that,this paper also studies the design SNR.Through data comparison,a robust design SNR is finally selected.Further,due to the unique encoding method of the polar codes,its code length is limited to the n power of 2.In order to make the design of polar codes more flexible and meet the needs of different scenarios,this paper deeply studies the method of achieving rate compatibility.Code rate compatibility can be achieved only by reasonably selecting the length of the information bits.In the code length compatible design,a puncturing(pruning)technique is used in this paper.Firstly,based on the quasi-uniform puncturing algorithm,this paper proposes an improved quasi-uniform fixed-bit puncturing method,which only punctures fixed bits.When the number of puncture bits is small,it achieves better performance than the original algorithm.Secondly,the generation matrix of the polar code is studied,and a punching method based on the minimum row weight of the generation matrix is proposed.Then,this paper proposes an improved puncturing algorithm based on channel reliability.The polarization code is layered first,and the worst channel in each layer is punctured.Finally,the advantages and disadvantages of the proposed several punching algorithms are analyzed and compared.In the part of decoding algorithm section,this paper first introduces the classic SC decoding,and then introduces its derived SCL decoding algorithm and CA-SCL decoding algorithm.After that,this paper analyzes the error detection and correction capabilities of CRC and proposes a CRC-assisted error detection and correction SCL decoding algorithm.This algorithm uses a lookup table in the middle of the information bits for error correction;at the end of the information,CRC is used for detection and verification.The algorithm reasonably utilizes the ignored CRC error correction capability,applies CRC error correction and detection to the decoding process at the same time,and achieves superior performance.