Blind Recognition of Cyclic Codes Based on Average Cosine Conformity
Zhaojun Wu, Zhaogen Zhong, Limin Zhang
Abstract
Channel coding technology is indispensable in digital communication systems. In noncooperative contexts, the blind identification of channel codes is very important. In this paper, a new algorithm that directly uses a soft-decision sequence for blind reconstruction of cyclic codes is proposed. From the algebraic structure of cyclic codes, we deduce that a cyclic code of length n must be able to divide the polynomial x <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> + 1, and the dual spaces corresponding to the factors of the generator polynomial can form a parity-check relation with the code words. In order to detect this relation, the concept of the average cosine conformity is defined, which can fully utilize the intercepted soft-decision sequence to measure the reliability of the parity-check relation. Further, the statistical characteristics of the average cosine conformity with respect to a candidate factor of the generator polynomial are analyzed in detail. When the traversal code length n is equal to the actual length, some factors in x <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> + 1 allow this constraint relation to be detected, and the generator polynomial of the cyclic codes consists of these factors. Hence, the blind reconstruction of the cyclic code is exactly equivalent to the hypothesis testing problem. Simulations show that the derived theoretical distribution of the average cosine conformity is consistent with the simulation results. Moreover, the proposed algorithm has preferable performance at low signal-to-noise ratios compared with existing methods, and its computational complexity is reasonable.