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.