Research On Secrecy Encoding Schemes Using Polar Code Over Gaussian Wiretap Channels

Polar code is a capacity-achievable block code with low encoding and decoding complexity.The construction of polar codes is strongly related to channel conditions.These characteristics make it perfectly appropriate for constructing secrecy coding scheme under wiretap channel.This thesis focuses on the research about encoding and decoding algorithms of the secrecy coding scheme using polar codes under Gaussian wiretap channel.This topic has important meaning both in theoretical study and practical applications.First,we studied on the encoding algorithms of the secrecy scheme using polar code over Gaussian wiretap channel.A secrecy coding scheme using polar codes under binary-input wiretap channel is proposed by Mahdavifar and Vardy,which can be regarded as a special case of the Coset-coding method.This method is named as the classic secrecy coding scheme in this thesis.However,under low-SNR channel conditions,the classic coding algorithm cannot guarantee the security using polar code with finite length.Moreover,it is difficult to find an appropriate value of the threshold of the information number to achieve a good tradeoff between the reliability and the security.Through theoretical and simulating analysis,we find that the value of message bits is the key of reliability and security.So,we give a rough range of the value of message bits.Furthermore,according to the block error rate of polar codes,we proposed a fast algorithm to find an accurate message bits value in the Gaussian wiretap channel.Simulation results show that the secrecy coding scheme with the proposed algorithm can achieve a good tradeoff between the reliability and the security.Then,we studied decoding algorithms of the secrecy scheme using polar code over Gaussian wiretap channel.In the Segmented Cyclic Redundancy Check Aided Successive Cancellation List(SCA-SCL)decoding algorithm,the message sequence is divided into several segments and a CRC code is added to each segment.Since the CRC detector is taken as the stopping criterion of the decoding process,the computational complexity of SCA-SCL decoding algorithm is low.By analyzing the trend of the Log of Likelihood Ratio(LLR)and Path Metric Unit(PMU)in the decoding procedure,we proposed two improved SCA-SCL decoding algorithms,List-Reduced(LR)SCA-SCL and Split-Reduced(SR)SCA-SCL.Simulation results show that when the number of segments with the same length is 4,the proposed LR-SCA-SCL decoding algorithm achieves 70%computational complexity reduction with the cost of 0.8dB decoding performance degradation,and the SR-SCA-SCL decoding algorithm achieves 33%computational complexity reduction with the cost of 0.2dB decoding performance degradation,where the performance of the CA-SCL decoding algorithm is compared.