Research On Coding And Decoding Of Raptor Fountain Codes Based On Polar Codes

Effectiveness and reliability are two criteria for measuring the performance of a communication system,where reliability can be obtained by channel coding,but this reliability comes at the expense of effectiveness.The Polar code was proposed by Professor E.Arikan of Turkey in 2009.The only one that can be proved by theory is that when the code length tends to infinity,the performance can reach the channel coding of Shannon.For the Polar code,although the long code has good performance,the performance of the Polar code is not very good for medium and long codes as well as short codes.In the 3GPP 5G-NR standard,it is determined that in the eMBB scenario,the Polar code is used as a short code of the control channel.Although the short Polar code is not as good as the long code,the performance of the short Polar code is better than low density parity check code(LDPC),Turbo code,and Tail-biting Convolution Code(TBCC)in the case of the same code length.The Raptor fountain code currently in use was proposed by Qualcomm in 2009,which is a channel code that is cascaded by an LDPC code and an LT fountain code.Since the Polar code has better performance than the LDPC for the short code,it is natural to think of using a better performance Polar code instead of the LDPC to obtain a new type of better performance Raptor code.First of all,this paper introduces the basic principles of Polar code,including channel polarization and the construction of generator matrix according to channel polarization theory,channel reliability estimation,information bit selection and polarization code encoding algorithm,and polarization code decoding algorithm.Then introducing the basic principles of the fountain code,including the fountain code degree distribution function,LT fountain code encoding,LT fountain code soft decision and hard decision BP decoding algorithm,Raptor code encoding and decoding algorithm.Next,introducing the basic principle of the product code,including the coding algorithm of the product code and the decoding algorithm are introduced.Secondly,by analyzing the channel polarization of the polarization code and the generation matrix structure,the equivalence of the none bit-reversed Polar code and the bit-reversed Polar code is theoretically proved.The boundary structure of the bit-free inverted Polar code and the SC decoding structure are given,and the corresponding iterative decoding formula is given.The use of a none bit-reversed Polar code can reduce the encoding and decoding implementation complexity of the Polar code.Then the Raptor fountain code based on Polar code is proposed.The Polar code uses SC decoding algorithm and the fountain code makes soft decision BP decoding algorithm.Subsequently,a Polar code-based Raptor fountain code with a product code structure is proposed.The Polar code uses the SC decoding algorithm,and the fountain code makes soft decision BP decoding algorithm.Finally,the Matlab simulation image of the relevant coding is given,including related simulation of Polar code,related simulation of LT fountain code,correlation simulation of Polar code based on Polar code,and correlation simulation of Polar code based on Polar code with product code structure,and comparing the performance difference of different codes.Thus,the final conclusion of this paper is obtained.