Research On Encoding And Decoding Algorithms Of Convolutional Polar Codes

Polar codes(PCs)are constructed by channel polarization method,which are the first coding scheme that can be strictly proved to achieve the Shannon limit of binary input symmetric discrete memoryless channels,so they have attracted extensive attention of scholars.Convolutional polar codes(CPCs)are a new polarization coding scheme produced by replacing block polarization kernel with convoluted kernel,which can obtain better channel polarization and error correction performance than polar codes.Therefore,the research of convolutional polar codes is of great significance to the further development of channel coding technology in the future.This thesis mainly studies the encoding and decoding algorithms of convolutional polar codes.A novel segmented cyclic redundancy check-aided successive cancellation list(SCA-SCL)decoding algorithm is proposed,and the performance of convolutional polar codes in fading channels is studied and analyzed.The specific research work is as follows:Aiming at the cyclic redundancy check(CRC)aided list decoding algorithm of convolutional polar codes,a new segmented CRC-aided successive cancellation list decoding algorithm based on reliability distribution is proposed.Firstly,the reliability of each subchannel is obtained according to Monte Carlo simulations.Then,the sliding window algorithm is used to search the consecutive subchannel with the lowest reliability as the segmentation point,that is,the CRC check sequence is added at the most error tolerant position.Based on this multi-CRC structure,each segment is decoded and CRC is detected in turn in the decoding stage.If there is an error in the decoding of a certain information segment,the decoding will be terminated directly;otherwise continue to the next segment until the end.Thus,the decoding error can be detected in time in the decoding stage and the correct path can be saved to the greatest extent.The simulation under binary input Gaussian white noise channel shows that compared with the traditional single segment cyclic redundancy check-aided list decoding algorithm and the uniform segment cyclic redundancy check-aided list decoding algorithm,the proposed decoding algorithm can obtain better frame error performance and lower decoding complexity.In addition,the algorithm is suitable not only for convolutional polar codes,but also for polar codes.For the performance analysis of convolutional polar codes in fading channel,this thesis makes theoretical and simulation analysis for fast fading and block fading respectively.The construction of convolutional polar codes in fast fading channel is relatively simple,and the construction method of polar codes can be directly extended.The reliability of subchannel can still be obtained through Monte Carlo simulations,and then the information set can be obtained.In block fading channel,it is necessary to conduct Monte Carlo simulation in different intervals according to the signal-to-noise ratio,so as to obtain the reliability of subchannels in the corresponding interval,then acquire the corresponding information set.In addition,this thesis focuses on the upper bound of error probability of convolutional polar codes in polarization channel for block mapping and random mapping.Due to the asymmetric encoding and decoding structure of convolutional polar codes,simulation analysis shows that when the number of fading blocks is 2,convolutional polar codes can obtain diversity gain under block mapping,but can not obtain diversity gain under random mapping.This result is just opposite to the performance of polar codes under the two mapping modes.When the number of fading blocks is greater than or equal to 3,the performance of convolutional polar codes in the two mapping methods is basically the same,and both can obtain diversity gain.