线性扰码重建算法性能分析
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摘要
线性扰码通常由线性反馈移位寄存器生成,非合作通信方需要对扰码参数进行盲估计才能恢复信息序列。为了有效解决扰码重建算法的适用性问题,通过对Walsh-Hadamard变换的扰码重建算法性能进行理论研究,分析影响扰码重建算法性能的相关因素。首先,基于假设检验,分析了反馈关系检测的误判概率,将误判概率解析表示为接收数据量、信源有偏性和反馈多项式重量的函数;其次,在误判概率给定的情况下,进行了数据量需求分析;最后,讨论了算法复杂度,为工程应用和下一步进行线性扰码重建算法研究提供理论依据。
A linear scrambler was usually defined based on a linear feedback shift register(LFSR).An eavesdropper must reconstruct the scrambler of the communication scheme to recover the information sequence.In order to effectively solve the problem of the applicability of the scrambler reconstruction,the performance of an algorithm based on Walsh-Hadamard transformation is theoretically studied,and the related factors affecting the algorithm are analyzed.Firstly,we express the misjudgment probability as a function of the amount of received data,the bias of information sequence and the weight of feedback polynomial.Secondly,when a misjudgment probability is given,we analyze the required amount of received data to meet the performance demand.Finally,we discuss the algorithm complexity.This work provides a theoretical basis for engineering applications and further studies on the reconstruction of linear scrambler.
A linear scrambler was usually defined based on a linear feedback shift register(LFSR).An eavesdropper must reconstruct the scrambler of the communication scheme to recover the information sequence.In order to effectively solve the problem of the applicability of the scrambler reconstruction,the performance of an algorithm based on Walsh-Hadamard transformation is theoretically studied,and the related factors affecting the algorithm are analyzed.Firstly,we express the misjudgment probability as a function of the amount of received data,the bias of information sequence and the weight of feedback polynomial.Secondly,when a misjudgment probability is given,we analyze the required amount of received data to meet the performance demand.Finally,we discuss the algorithm complexity.This work provides a theoretical basis for engineering applications and further studies on the reconstruction of linear scrambler.
引文
[1]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 Z L,PENG H,GONG K X,et al.Scrambler blind recognition method based on soft information[J].Journal on Communication,2017,38(3):174-182.
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[9]尹瑾,王建新.基于软判决求解含错方程的自同步扰码盲识别[J].探测与控制学报,2017,39(2):44-48.YIN J,WANG J X.Self-synchronous scrambler blind recognition based on soft-decision solving error-containing equation[J].Journal of Detection&Control,2017,39(2):44-48.
[10]吕喜在,苏绍璟,黄芝平.一种新的自同步扰码多项式盲恢复方法[J].兵工学报,2011,32(6):680-685.LX Z,SU S J,HUANG Z P.A novel blind recovery method of self-synchronizing scrambling polynomial[J].Acta Armamentarii,2011,32(6):680-685.
[11]赵知劲,李淼,詹毅.LSC-DSSS信号长短伪码盲估计[J].信号处理,2016,32(3):268-275.ZHAO Z J,LI M,ZHAN Y.Blind estimation of long and short PN code in LSC-DSSS signals[J].Journal of Signal Processing,2016,32(3):268-275.
[12]黄芝平,周靖,苏绍璟,等.基于游程统计的自同步扰码多项式阶数估计[J].电子科技大学学报,2013,42(4):541-545.HUANG Z P,ZHOU J,SU S J,et al.Order estimation of self-synchronizing scrambling polynomial based on run statistic[J].Journal of University of Electronic Science and Technology of China,2013,42(4):541-545.
[13]游凌,朱中梁.Walsh函数在解二元域方程组上的应用[J].信号处理,2000,16(S1):27-30,20.YOU L,ZHU Z L.The application of Walsh function in resolving of F(2)equations[J].Signal Processing,2000,16(S1):27-30,20.
[14]CLUZEAU M.Reconstruction of a linear scrambler[J].IEEE Trans.on Computers,2007,56(9):1283-1291.
[15]LIU X B,KOH S N,WU X W,et al.Reconstruction of a linear scrambler with improved detection capability and in the presence of noise[J].IEEE Trans.on Information Forensics and Security,2012,7(1):208-218.
[16]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 Trans.on Information Forensics and Security,2013,8(3):542-552.
[17]HAN S N,ZHANG M,LI X H.Reconstruction of feedback polynomial of synchronous scrambler based on triple correlation characteristics of M-sequences[J].IEICE Trans.on Communications,2018,101(7):1723-1732.
[18]VALEMBOIS A.Detection and recognition of a binary linear code[J].Discrete Applied Mathematics,2001,111(1/2):199-218.
[19]BRUSHE G D,WAX M,WHITE L B.Determining the constraint length and generating polynomials of rate 1/L convolutional coded signals[J].IEEE Signal Processing Letters,1995,2(8):160-162.
[20]LU P Z,LI S,ZOU Y,et al.Blind recognition of punctured convolutional codes[J].Science in China Series F,2005,48(4):484-498.
[21]MARAZIN M,GAUTIER R,BUREL G.Blind recovery of k/n rate convolutional encoders in a noisy environment[J].Eurasip Journal on Wireless Communications&Networking,2011,2011:168.
[22]MARAZIN M,GAUTIER R,BUREL G.Algebraic method for blind recovery of punctured convolutional encoders from an erroneous bitstream[J].IET Signal Processing,2012,6(2):122-131.
[23]YU P D,LI J,PENG H.A least square method for parameter estimation of RSC sub-codes of Turbo codes[J].IEEE Communication Letters,2014,18(4):644-647.
[24]YU P D,PENG H,LI J.On blind recogniton of channel codes within a candidate[J].IEEE Communication Letter,2016,20(4):736-739.
[25]HUANG L,CHEN W G,CHEN E H,et al.Blind recognition of k/n rate convolutional encoders from noisy observation[J].Journal of Systems Engineering and Electronics,2017,2(28):235-243.
[26]XIA T,WU H C.Novel blind identification of LDPC codes using average LLR of syndrome a posteriori probability[J].IEEE Trans.on Signal Processing,2014,62(3):632-640.
[27]MOOSAVI R,LARSSON E G.Fast blind recognition of channel codes[J].IEEE Trans.on Communications,2014,62(5):1393-1405.
[28]SOTEH A G,BIZAKI H K.On the analytical solution of rank problem in the convolutional code identification context[J].IEEE Communications Letters,2016,20(3):644-647.
[29]ZHOU J,HUANG Z P,SU S J,et al.Blind identification of convolutional codes in soft-decision situations[J].International Journal of Modern Communications Technologies Research,2014,2(4):4-6.
[30]SU S J,ZHOU J,HUANG Z P,et al.Blind identification of convolutional encoder parameters[J].Scientific World Journal,2014,2014:1-9.
[2]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 Y,ZHANG L M.Reconstruction of scrambler with realtime test[J].Journal of Electronics&Information Technology,2016,38(7):1794-1799.
[3]MA Y,ZHANG L M,WANG H T.Reconstructing synchronous scrambler with robust detection capability in the presence of noise[J].IEEE Trans.on Informaiton Forensics and Security,2015,10(2):397-408.
[4]XIE H,WANG F H,HUANG Z T.Blind reconstruction of linear scrambler[J].Journal of Systems Engineering and Electronics,2014,25(4):560-565.
[5]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 X Y,SHEN L,LU P Z,et al.Fast blind restore of LFSR sequences with high error tolerance[J].Signal Processing,2004,20(6):552-558.
[6]解辉,韩壮志,丁爽.基于传播算子算法的扰码序列估计方法[J].系统工程与电子技术,2017,39(10):2327-2332.XIE H,HAN Z Z,DING S.Estimation of scrambler based on propagator method[J].Systems Engineering and Electronics,2017,39(10):2327-2332.
[7]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 Y,ZHANG L M,WANG H T.Blind identification of frame synchronization in scrambled coding sequence[J].Acta Electronica Sinica,2016,44(9):2087-2092.
[8]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.
[9]尹瑾,王建新.基于软判决求解含错方程的自同步扰码盲识别[J].探测与控制学报,2017,39(2):44-48.YIN J,WANG J X.Self-synchronous scrambler blind recognition based on soft-decision solving error-containing equation[J].Journal of Detection&Control,2017,39(2):44-48.
[10]吕喜在,苏绍璟,黄芝平.一种新的自同步扰码多项式盲恢复方法[J].兵工学报,2011,32(6):680-685.LX Z,SU S J,HUANG Z P.A novel blind recovery method of self-synchronizing scrambling polynomial[J].Acta Armamentarii,2011,32(6):680-685.
[11]赵知劲,李淼,詹毅.LSC-DSSS信号长短伪码盲估计[J].信号处理,2016,32(3):268-275.ZHAO Z J,LI M,ZHAN Y.Blind estimation of long and short PN code in LSC-DSSS signals[J].Journal of Signal Processing,2016,32(3):268-275.
[12]黄芝平,周靖,苏绍璟,等.基于游程统计的自同步扰码多项式阶数估计[J].电子科技大学学报,2013,42(4):541-545.HUANG Z P,ZHOU J,SU S J,et al.Order estimation of self-synchronizing scrambling polynomial based on run statistic[J].Journal of University of Electronic Science and Technology of China,2013,42(4):541-545.
[13]游凌,朱中梁.Walsh函数在解二元域方程组上的应用[J].信号处理,2000,16(S1):27-30,20.YOU L,ZHU Z L.The application of Walsh function in resolving of F(2)equations[J].Signal Processing,2000,16(S1):27-30,20.
[14]CLUZEAU M.Reconstruction of a linear scrambler[J].IEEE Trans.on Computers,2007,56(9):1283-1291.
[15]LIU X B,KOH S N,WU X W,et al.Reconstruction of a linear scrambler with improved detection capability and in the presence of noise[J].IEEE Trans.on Information Forensics and Security,2012,7(1):208-218.
[16]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 Trans.on Information Forensics and Security,2013,8(3):542-552.
[17]HAN S N,ZHANG M,LI X H.Reconstruction of feedback polynomial of synchronous scrambler based on triple correlation characteristics of M-sequences[J].IEICE Trans.on Communications,2018,101(7):1723-1732.
[18]VALEMBOIS A.Detection and recognition of a binary linear code[J].Discrete Applied Mathematics,2001,111(1/2):199-218.
[19]BRUSHE G D,WAX M,WHITE L B.Determining the constraint length and generating polynomials of rate 1/L convolutional coded signals[J].IEEE Signal Processing Letters,1995,2(8):160-162.
[20]LU P Z,LI S,ZOU Y,et al.Blind recognition of punctured convolutional codes[J].Science in China Series F,2005,48(4):484-498.
[21]MARAZIN M,GAUTIER R,BUREL G.Blind recovery of k/n rate convolutional encoders in a noisy environment[J].Eurasip Journal on Wireless Communications&Networking,2011,2011:168.
[22]MARAZIN M,GAUTIER R,BUREL G.Algebraic method for blind recovery of punctured convolutional encoders from an erroneous bitstream[J].IET Signal Processing,2012,6(2):122-131.
[23]YU P D,LI J,PENG H.A least square method for parameter estimation of RSC sub-codes of Turbo codes[J].IEEE Communication Letters,2014,18(4):644-647.
[24]YU P D,PENG H,LI J.On blind recogniton of channel codes within a candidate[J].IEEE Communication Letter,2016,20(4):736-739.
[25]HUANG L,CHEN W G,CHEN E H,et al.Blind recognition of k/n rate convolutional encoders from noisy observation[J].Journal of Systems Engineering and Electronics,2017,2(28):235-243.
[26]XIA T,WU H C.Novel blind identification of LDPC codes using average LLR of syndrome a posteriori probability[J].IEEE Trans.on Signal Processing,2014,62(3):632-640.
[27]MOOSAVI R,LARSSON E G.Fast blind recognition of channel codes[J].IEEE Trans.on Communications,2014,62(5):1393-1405.
[28]SOTEH A G,BIZAKI H K.On the analytical solution of rank problem in the convolutional code identification context[J].IEEE Communications Letters,2016,20(3):644-647.
[29]ZHOU J,HUANG Z P,SU S J,et al.Blind identification of convolutional codes in soft-decision situations[J].International Journal of Modern Communications Technologies Research,2014,2(4):4-6.
[30]SU S J,ZHOU J,HUANG Z P,et al.Blind identification of convolutional encoder parameters[J].Scientific World Journal,2014,2014:1-9.