Polar Code Optimization Design And FPGA Implementation

Shannon's theorem calculates the maximum transmission rate of the communication channel.After so many years of development,the channel coding scheme that can achieve the Shannon limit has not yet appeared.Until Erdal Arikan proposed the theory of channel polarization in 2008,this situation has changed.The polar code is currently the only channel coding method that can be mathematically proved to reach the Shannon limit and has low incodong and decoding complexity.Therefore,it has attracted widespread attention.In addition,it has been found that channel polarization is widespread in many communication scenarios,which is also in line with the large-capacity requirements of 5G communication.And it has considerable development prospects in the future 5G communication.Through the continuous efforts of channel coding scholars,the current error correction performance of the polarization code can exceed the currently widely used Turbo code and LDPC code.However,the introduction of polar code is relatively late,and there are still many problems that need to be solved and improved.For example,how to overcome frequent polarization problems,high-speed decoding problems of polar code,and rate-compatible design of polar code in a communication system with rapidly changing channels.In this paper,the scheme of polarization code rate compatible design is studied,and it is verified on the hardware platform to realize variable rate and variable rate polarization code encoding and decoding system.First of all,this paper systematically studies the basic principles of polar code.The phenomenon of channel polarization is introduced in detail,and the process of channel combination and channel splitting in polarization is analyzed.The similarity between the fast Fourier transform process and the polarization code encoding process is analyzed,and the pipelined encoder structure is given based on this.The selection of reliable channel in the polar code directly relates to the reliability of communication.Therefore,the two methods of Barcol parameters and Gaussian approximation in channel reliability estimation are analyzed.And then the advantages and disadvantages of the two are summarized.The Gaussian approximation scheme is more suitable for practical AWGN channel.Secondly,the SC decoding algorithm of polarization code is analyzed and studied.According to the relevant conclusions in channel polarization,the recursive formula of SC decoding algorithm is studied,and the scheme of reducing the hardware implementation complexity is analyzed in the logarithmic domain.The scheme of the code rate adaptability of the polarization code is studied,including quasi-uniform puncturing and channel-based reliability puncturing.The performance of the two methods is compared to prove that the later is more valuable for the performance of polar code.Finally,the hardware implementation architecture of the polarization code encoding and decoding algorithm are proposed.The quantization scheme used in the simulation and the internal details of each module in the whole system are given.The hardware result is as same as the results in MATLAB are consistent,which verifies the achievability of the rate adaptive scheme.