Abstract：The existing methods need to know a priori dual word of a convolutional code to reconstruct the feedback polynomial of a synchronous scrambler placed after a convolutional encoder.To overcome this limitation,a novel reconstruction method is proposed based on the triple correlation property of m-sequences.First,the scrambled bit sequence is divided into multiple blocks.The length of each block equals the constraint length of the convolutional encoder,and the interval between two start points of adjacent blocks is the codeword length.Then,it is proved that the generated sequence by the dot product of scrambled bit blocks with a dual word is also an m-sequence,having the same period as the synchronous scrambler.With this result,a dual word of the convolutional encoder can be estimated based on the triple correlation property of m-sequences.Finally,the feedback polynomial is reconstructed by using two locations of triple correlation peaks.For the case that there are bit errors in the received sequence,the probability distributions of the peak and non-peak values of triple correlation are derived.Therefore,the threshold for detecting triple correlation peaks is obtained,and the confidence level of the correct reconstruction is analyzed.Simulation results show the effectiveness of the proposed method.Compared with the existing methods,the proposed method does not require the prior knowledge of a dual word and eliminates the uncertainty in the reconstruction results.Moreover,the proposed method is more robust to bit errors.
韩树楠, 张旻, 李歆昊. 基于m序列三阶相关性的同步扰码反馈多项式重构[J]. 电子学报, 2019, 47(3): 552-559.
HAN Shu-nan, ZHANG Min, LI Xin-hao. Reconstruction of Feedback Polynomial of Synchronous Scrambler Placed after Convolutional Encoder Based on Triple Correlation Property of m-Sequences. Acta Electronica Sinica, 2019, 47(3): 552-559.
[1] 解辉,黄知涛,王丰华.信道编码盲识别技术研究进展[J].电子学报,2013,41(6):1166-1176.XIE Hui,HUANG Zhi-tao,WANG Feng-hua.Research progress of blind recognition of channel code[J].Acta Electronica Sinica,2013,41(6):1166-1176.(in Chinese)
[2] 李相迎.CCSDS数据链路层协议识别关键技术研究[D].北京:中国科学院空间科学与应用研究中心,2011.LI Xiang-ying.Key technologies of protocol identification for CCSDS data link layer[D].Beijing:Center for Space Science and Applied Research Chinese Academy of Sciences,2011.(in Chinese)
[3] JONSSON F,JOHANSSON T.Theoretical analysis of a correlation attack based on convolutional codes[J].IEEE Transactions on Information Theory,2002,48(8):2173-2181.
[4] FOSSORIER M,MIHALJEVIC M,IMAI H.A unified analysis for the fast correlation attack[A].Proceedings of International Symposium on Information Theory[C].Adelaide,SA,Australia:IEEE,2005.2012-2015.
[5] MASSEY J.Shift-register synthesis and BCH decoding[J].IEEE Transactions on Information Theory,1969,15(1):122-127.
[6] 罗向阳,沈利,陆佩忠,等.高容错伪随机扰码的快速盲恢复[J].信号处理,2004,20(6):552-558.LUO Xiang-yang,SHEN Li,LU Pei-zhong,et al.Fast blind restore of LFSR sequences with high error toleranc[J].Signal Processing,2004,20(6):552-558.(in Chinese)
[7] 伍文君,黄芝平,唐贵林,等.含错扰码序列的快速恢复[J].兵工学报,2009,30(8):1134-1138.WU Wen-jun,HUANG Zhi-ping,TANG Gui-lin,et al.Fast recovery of interfered scrambling code sequence[J].Acta Armentarii,2009,30(8):1134-1138.(in Chinese)
[8] 马钰,张立民.基于实时检测的扰码重建算法[J].电子与信息学报,2016,38(7):1794-1799.MA Yu,ZHANG Li-min.Reconstruction of Scrambler with real-time test[J].Journal of Electronics & Information Technology,2016,38(7):1794-1799.(in Chinese)
[9] XIE H,WANG F H,HUANG Z.Blind reconstruction of linear scrambler[J].Journal of Systems Engineering and Electronics,2014,25(4):560-565.
[10] 郝士琦,戚林,王勇.一种新的伪随机扰码盲识别方[J].电路与系统学报,2011,16(4):6-12.HAO Shi-qi,QI Lin,WANG Yong.A new blind recognition method of pesudo-randomizer code sequence[J].Journal of Circuits and Systems,2011,16(4):6-12.(in Chinese)
[11] 吕全通,张旻,朱宇轩.基于相关度统计的同步扰码盲识别方法[J].数据采集与处理,2016,31(3):570-576.Lü Quan-tong,ZHANG Min,ZHU Yu-xuan.Blind recognition method for synchronous scrambler based on statistical correlation[J].Journal of Data Acquisition and Processing,2016,31(3):570-576.(in Chinese)
[12] CLUZEAU M.Reconstruction of a linear scrambler[J].IEEE Transactions on Computers,2007,56(9):1283-1291.
[13] LIU X B,KOH S N,WU X W,et al.Reconstructing a linear scrambler with improved detection capability and in the presence of noise[J].IEEE Transactions on Information Forensics and Security,2012,7(1):208-218.
[14] HE W J.Reconstructing the feedback polynomial of a linear scrambler with the method of hypothesis testing[J].IET Communications,2015,9(8):1044-1047.
[15] 陈泽亮,彭华,巩克现,等.基于软信息的扰码盲识别方法[J].通信学报,2017,38(3):174-182.CHEN Ze-liang,PENG Hua,GONG Ke-xian,et al.Scrambler blind recognition method based on soft information[J].Journal on Communications,2017,38(3):174-182.(in Chinese)
[16] 于沛东,李静,彭华.一种利用软判决的信道编码识别新算法[J].电子学报,2013,41(2):301-306.YU Pei-dong,LI Jing,PENG Hua.A novel algorithm for channel coding recognition using soft-decision[J].Acta Electronica Sinica,2013,41(2):301-306.(in Chinese)
[17] LIU X B,KOH S N,CHUI C C,et al.A study on reconstruction of linear scrambler using dual words of channel encoder[J].IEEE Transactions on Information Forensics and Security,2013,8(3):542-552.
[18] MA Y,ZHANG L M,WANG H T.Reconstructing synchronous scrambler with robust detection capability in the presence of noise[J].IEEE Transactions on Information Forensics and Security,2015,10(2):397-408.
[19] 马钰,张立民,王好同.编码加扰序列的帧同步盲识别[J].电子学报,2016,44(9):2087-2092.MA Yu,ZHANG Li-min,WANG Hao-tong.Blind identification of frame synchronization in scrambled code sequence[J].Acta Electronic Sinica,2016,44(9):2087-2092.(in Chinese)
[20] AHMAD G S,HOSSEIN K B.On the analytical solution of rank problem in the convolutional code identification context[J].IEEE Communications Letters,2016,20(3):442-445.
[21] 白彧,杨晓静,张玉.基于高阶统计处理技术的m-序列帧同步码识别[J].电子与信息学报,2012,34(1):33-37.BAI Yu,YANG Xiao-jing,Zhang Yu.A recognition method of m-sequence synchronization codes using higher-order statistics processing[J].Journal of Electronics & Information Technology,2012,34(1):33-37.(in Chinese)
[22] 赵知劲,顾骁炜,沈雷,等.非周期长码直扩信号的伪随机码盲估计[J].通信学报,2015,36(5):27-34.ZHAO Zhi-jin,GU Xiao-Wei,SHEN Lei,et al.Blind estimation of pseudo-random codes in non-periodic long code direct-sequence spread-spectrum signals[J].Journal of Communications,2015,36(5):27-34.(in Chinese)
[23] BATTY K E,ADAMS E R.Detection and blind identification of m-sequence codes using higher order statistics[A].Proceedings of Signal Processing Workshop on Proceedings of the Higher-Order Statistics[C].Caesarea,Israel:IEEE,1999.16-20.
2019, Vol. 47 
