Reconstruction of a Synchronous Scrambler Based on Average Check Conformity

Abstract

Channel coding technology is indispensable in digital communication systems. In noncooperative contexts, the identification of the channel codes of the synchronous scrambler is essential. In this paper, a new algorithm that directly uses a soft decision sequence for blind reconstruction of the synchronous scrambler is proposed. First, considering imbalanced signal sources and the principle of scrambling and descrambling the synchronous scrambler, the error-containing equation of the synchronous scrambler is established. Second, the average check conformity is introduced to complete the check relationship detection. Then, based on the statistical characteristics of the average check conformity, the corresponding discrimination threshold is established, and the reconstruction of the feedback polynomial of the synchronous scrambler is completed by traversing the possible primitive polynomials. Finally, the verification equation is determined by the method of subsection optimization, which greatly reduces the number of initial states that need to be traversed; this is critical for scramblers with high-order feedback polynomials (i.e., when the order of the feedback polynomial is greater than 15). Simulations show that the algorithm can effectively reconstruct the synchronous scrambler under imbalanced signal sources. Moreover, the proposed algorithm offers improved performance with about 1–2 dB gain at low signal-to-noise ratios compared with existing methods, and its computational complexity is reasonable.