Research On Algorithm Of Encoding And Decoding For Polar Codes In AWGN Channel

In systems of modern communication,the method of channel code has been applied to improve the performance of the digital communication systems,which could bring the code gain and impro ve the capacity of the communication systems.With the development of channel code technology,researchers have been working to optimize code scheme,as known as that the coding scheme of channel capacity could approach the C.E.Shannon's theoretical limit.E.Arikan(2009)proposed polar code is the first class of provable capacity-achieving for binary discrete memoryless channels when the code length goes into infinity.This article is based principle of polar code coding and decoding to design the theory of polar code in AWGN channel.The main achievements are summarized as followings:1.This study investigated channels in the process of polarization in two key steps: channel combine and channel split.Via mathematical theory and information theory related theoretical basis in detail,this study elaborated the coding principle of polar code and simulated the property of the channel polarization.This study also introduces the successive cancellation decoding algorithm,the successive cancellation list decoding algorithm and the belief propagation decoding algorithm briefly.Finally,this investigations also analyzes the performance of polar code decoding and the complexity of coding and decoding in theory.2.Research on Two-Threshold Quantization Algorithm for AWGN Channel in application of polar code.In order to achieve the classic polar code in different channels,the AWGN channel is quautized into approximation binary erasure in order to quantify the misjudgment probability of the quantization erasure channel as the objective function.The simulation results indicate that compared with other schemes,the AWGN channel with two-threshold quantization can be effectively quantized as an approximate binary erasure channel.Finally,the polar code decoding using the two-threshold quantization algorithm has a lower bit error rate.3.To solve the problem of channel polarization process that has not been completely polarized neutron channel,the mathematical expectation of the logarithmic likelihood ratio of each sub-channel probability density function,the study proposes to measure the channel polarization effect of AWGN approximate polar code algorithm.With combination of the Gaussian approximation of low density parity check code,this research generates iterative equation.The simulation results show that the AWGN channel approximation polar code algorithm has better polarization performance and lower complexity and lower bit error rate compared with Monte-Carlo algorithm.