Reconstructing Synchronous Scrambler With Robust Detection Capability in the Presence of Noise

Considering the channel noise was present, we presented techniques to reconstruct the feedback polynomial as well as the initial state of a scrambler placed after a channel encoder. The previous algorithms could not keep the detection performance over the design requirements, such as a false-alarm probability. Thus, we proposed a modified scheme to improve the detection capability. With multiple output sequences of matched filter that were scrambled by the same scrambler, we reduced the number of samples required for the reconstruction of the feedback polynomial when the signal-to-noise ratio was <0 dB. Meanwhile, we proposed a scheme to restore the initial state of the scrambler in the presence of channel noise. We also developed two lemmas and two theorems to reconstruct the synchronous scrambler with block summation. Following the lemmas and the theorems, we could use the blocks to generate a new sequence with certain method such as multiplying a dual word, and detect the optimal multiple of the original scrambler’s feedback polynomial, or even the correct one.