Research On Hybrid Polar Codes And Implementation Of FPGA

The polar code is a new linear block code that was proposed by Arikan based on the mutual information chain rule.Arikan proved that if the Successive Cancellation(SC)decoding algorithm is used to decode,the decoding performance can reach the channel capacity when the code length is infinite in his thesis.The coding codeword of the polar code can be obtained by the information sequence and the generated matrix.As long as the polarized nucleus and code length of the polar code are given,its generated matrix can also be uniquely determined,and the complexity of solving the generated matrix is only (log ).Although the Successive Cancellation decoding algorithm is not the best decoding method,its decoding performance has a good gradation for the decoding performance of maximum likelihood decoding.The complexity of the Successive Cancellation decoding algorithm is only (log ),very low,which is a nearly linear relationship with the code length .The polar code has the advantages of generated matrix determination,low complexity of coding and decoding,so it has a good prospect in research and application.The main research contents and innovations of this article are as follows:(1)The reason why the Successive Cancellation decoding algorithm needs to bit-by-bit decoding is analyzed,and the parallelization is studied.It is found that the Successive Cancellation decoding algorithm can partially have parallel decoding under certain conditions through research.A recursive Successive Cancellation decoding algorithm is proposed for this feature,and then the bit error rate and operation time are analyzed by simulation.(2)The decoding process is analyzed by combining the code tree with the Successive Cancellation decoding algorithm.The essence of Successive Cancellation decoding algorithm is found through research.Its essence is to take the probability sum of all decoding paths under the code tree node as the basis for path pruning.On this basis,the successive cancellation decoding algorithm is improved.The maximum probability of all decoding paths under the code tree node is taken as the basis of path pruning instead of the probability sum.Then,the decoding performance and complexity of the algorithm are compared through simulation.(3)The restriction of classical second-order polarized nucleus on code length and code rate is analyzed.It is proposed that different polarized nucleus can be used to remove the restriction.The effects of third-order polarized nucleus and hybrid polarized nucleus on coding and decoding are studied.Combined with the chain rule of mutual information,the polarization process is studied.The coding and decoding methods of the third-order polarized nucleus and the hybrid polarized nucleus are studied and proposed.Comparing the decoding performance of classical second-order polarized nucleus,third-order polarized nucleus and hybrid polarized nucleus at different SNR.The hardware implementation of polar codes is studied and specific implementation methods are given.