Reconstruction of Feedback Polynomial of Synchronous Scrambler Based on Triple Correlation Characteristics of M-Sequences

Shu nan HAN  Min ZHANG  Xin hao LI  

IEICE TRANSACTIONS on Communications   Vol.E101-B   No.7   pp.1723-1732
Publication Date: 2018/07/01
Publicized: 2018/01/16
Online ISSN: 1745-1345
DOI: 10.1587/transcom.2017EBP3173
Type of Manuscript: PAPER
Category: Wireless Communication Technologies
synchronous scrambler,  convolutional code,  m-sequence,  triple correlation characteristic,  dual word,  

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For the reconstruction of the feedback polynomial of a synchronous scrambler placed after a convolutional encoder, the existing algorithms require the prior knowledge of a dual word of the convolutional code. To address the case of a dual word being unknown, a new algorithm for the reconstruction of the feedback polynomial based on triple correlation characteristic of an m-sequence is proposed. First, the scrambled convolutional code sequence is divided into bit blocks; the product of the scrambled bit blocks with a dual word is proven to be an m-sequence with the same period as the synchronous scrambler. Second, based on the triple correlation characteristic of the generated m-sequence, a dual word is estimated; the generator polynomial of the generated m-sequence is computed by two locations of the triple correlation peaks. Finally, the feedback polynomial is reconstructed using the generator polynomial of the generated m-sequence. As the received sequence may contain bit errors, a method for detecting triple correlation peaks based on the constant false-alarm criterion is elaborated. Experimental results show that the proposed algorithm is effective. Ulike the existing algorithms available, there is no need to know a dual word a priori and the reconstruction result is more accurate. Moreover, the proposed algorithm is robust to bit errors.