Blind Identification of Self‐Synchronous Scramblers for Reed–Solomon Codes in Non‐Cooperative Communications Using Soft‐Decision Information

ABSTRACT

Blind identification of channel coding parameters is of paramount importance in non‐cooperative communication scenarios, where the receiver lacks prior knowledge of the transmitter's coding scheme. This paper specifically addresses the challenging problem of blindly identifying the feedback polynomial of a self‐synchronous scrambler applied to a Reed–Solomon (RS) code, a scenario commonly encountered in various communication standards. Existing methods, which primarily rely on matrix rank analysis, exhibit poor fault tolerance in the presence of channel noise and suffer from high computational complexity. To overcome these limitations, we propose a novel and improved fault‐tolerant identification method that leverages soft‐decision information. Firstly, we provide a rigorous theoretical proof establishing that if the reciprocal polynomial of a binary dual‐vector polynomial of the RS code is multiplied by the scrambler's feedback polynomial, the vector corresponding to the reciprocal of this product satisfies a parity‐check relationship with the rows of the scrambled sequence matrix. Building upon this foundational relationship, we construct an average parity check confidence metric from the received soft‐decision sequence. We then derive the exact theoretical statistical distribution of this metric under two distinct hypotheses: the presence of the correct scrambler and the absence thereof. Utilizing the minimum error probability criterion, we analytically derive the optimal detection threshold, thereby enabling high‐reliability identification of the scrambler's feedback polynomial. To validate the effectiveness and robustness of the proposed method, comprehensive simulations are conducted using a variety of RS codes, in conjunction with scramblers of different orders. The simulation results demonstrate that the proposed method achieves a significant performance gain of approximately 4 dB in fault tolerance compared to existing state‐of‐the‐art rank‐based methods. Moreover, the proposed algorithm eliminates the need for exhaustive descrambling trials, resulting in substantially lower computational complexity. The method also exhibits considerable robustness to inaccuracies in noise variance estimation and provides a flexible trade‐off between the required sequence length and the desired level of identification reliability. This work makes significant contributions to the field of non‐cooperative communication by providing a practical and efficient solution for blind scrambler identification in RS‐coded systems.