A Study on Reconstruction of Linear Scrambler Using Dual Words of Channel Encoder

In this paper, the reconstruction of the feedback polynomial as well as the initial state of a linear feedback shift register (LFSR) in a synchronous scrambler placed after a channel encoder is studied. The study is first based on the assumption that the channel is noiseless and then extended to the noisy channel condition. The dual words, which are orthogonal to the codewords generated by the channel encoder, are used in the reconstruction algorithm. The number of bits required by the new algorithm is compared with another recently proposed algorithm and results show that the number of bits required to do the reconstruction can be significantly reduced.