Analysis And Design Of Concatenated Polar Codes

Polar code is the first type of channel coding scheme that has been proved to be able to achieve the symmetric capacity of any binary discrete memoryless channel(B-DMC).Since it came out,it has received extensive attention from academia and industry.Due to its unsatisfactory error correction performance under limited code length,scholars have proposed a coding scheme of concatenating an outer code,so that the error correction performance of Polar codes can be improved,which can be compared with the best existing codes,such as low density parity check(LDPC)code and Turbo code compete.The minimum distance is an important indicator to measure the performance of the Polar code,which directly affects the error correction performance of the Polar code,especially the error correction performance under a high signal-to-noise ratio(SNR).From the perspective of the minimum distance,this article aims to optimize the design of a scheme that can increase the minimum distance of the concatenated Polar code,thereby improving the error correction performance of the concatenated Polar code.The specific work content can be summarized as:(1)The channel polarization phenomenon and Polar code encoding and decoding principles are introduced in detail,and then several classic concatenated Polar code schemes are introduced,and the simulation performance of different concatenated Polar code schemes is given.(2)Cyclic Redundancy Check(CRC)code is a concatenated Polar code scheme(concatenated CRC-Polar code)of the outer code,which is a classic concatenated Polar code scheme.Since the CRC code can eliminate the code words with the smallest distance in the Polar code,the distance spectrum of the Polar code is optimized,so that the concatenated CRC-Polar code has good error correction performance.In order to enable the CRC code to eliminate more minimum distance codewords,in view of the shortcomings of the current concatenated CRC-Polar code scheme,while considering the structure of the Polar code,the optimization of the CRC code and the CRC check bit position for the concatenated CRC-Polar.A new concatenated CRC-Polar code scheme is optimized for the influence of the code.In the proposed scheme,the minimum distance of the concatenated CRC-Polar code under partial code length is improved,so that the error correction performance of the concatenated CRC-Polar code is improved,especially under the high signal-to-noise ratio.(3)In the actual application process due to the high computational complexity of the SCL decoding algorithm,the overall computational efficiency of the algorithm is not high and there is a certain delay.In response to this problem,scholars have proposed a solution of concatenated.Polar code with multiple CRC code.This scheme can not only reduce the storage space and time delay of the algorithm through the improved SCL decoding algorithm,but also provide early stop gain,thereby improving the efficiency of the algorithm.However,this scheme also has a certain performance loss.In view of this situation,two feasible optimization schemes are proposed.The first scheme considers the impact of Polar code itself on the performance while optimizing the CRC code;The second scheme aims at the different number of minimum distance codewords generated by each piece of information bit set,and uses a longer CRC code to protect the information bit set segment that generates a larger number of minimum distance codewords.The simulation results show that the two different optimization schemes have improved the error correction performance of the concatenated Polar code protected by multiple CRC code while retaining the original advantages.