Advanced Encoding And Decoding Technology For Polar Codes

Wireless communication is an indispensable means of information transmission in modern society.Shannon's channel coding theorem proves that there exists a channel coding,which can achieve progressive error-free transmission at the rate of the channel capacity.This theorem also sets a goal for channel coding:design a capacity achievable code with practical complexity.In 2008,Arikan proposed Polar Codes,the first capacity coding scheme in history,which quickly attracted widespread attention.The excellent performance of Polar Codes makes it a strong candidate for the 5G communication standard.However,as a new coding scheme,Polar Codes still have many problems in practical application and further improvement is required.Based on this background,this paper studies the mathematical tools to analyze the performance of Polar Codes and its corresponding decoder.Furthermore,specific techniques that can be used to improve the performance of Polar Codes are also proposed.The relevant research contents are summarized as follows.This paper proposes a Generalized Gaussian Approximation algorithm based on the generalized median.The standard Gaussian approximation algorithm for analyzing the performance of the SC decoder requires the distribution of input LLR value to be a symmetry Gaussian variable.That condition is no longer satisfied in the SCL decoder.Attempting to provide mathematical tools for SCL decoding performance analysis,this paper carefully investigates the standard Gaussian Approximation algorithm.The proposed Generalized Gaussian approximation algorithm breaks through the limitation of symmetry conditions.Furthermore,the distribution of path metrics is also investigated.Based on conjecture,a Generalized Gaussian approximation with a little modification is proposed to obtain the approximate distribution of path metrics.The effectiveness of the algorithm is proved by simulation.The algorithm can provide a theoretical tool for SCL decoding performance through useful mathematical tools to provide support for further optimization of Polar Codes and SCL decoders.In this paper,efficient decoding algorithms of Polar Codes are studied.SCL decoder needs to frequently copy the decoding path information and sort and delete the decoding path,which results in high complexity and high hardware implementation overhead.In addition,the performance of SC decoder can be greatly improved by flipping the first error bit.As a result,a BP-SC hybrid decoding algorithm is proposed.The BP-SC hybrid decoder performs a quasi-maximum likelihood search on the critical set through the modified enhanced BP algorithm,and then sends the results into the SC decoder to obtain the complete result.The decoder does not require complex operations on the decoding path.Through simulation experiments and comparison with other common decoders,the BP-SC decoder shows good decoding performance.Finally,a distributed CRC-aided Polar Codes construction method based on intermediate values is proposed.Distributed check bits and freeze bits with check capability will be added to the uncoded sequence.This method improves the performance without major adjustment.Furthermore,the decoder acquires the ability to early terminate the decoding process when it is already failed,thereby reducing latency and energy consumption.In order to obtain the check bit value flexibly,this paper proposes a CRC algorithm that extracts the intermediate value from the CRC register at the position where the check is needed.