Abstract: In order to address the drawbacks of recognition algorithm used for recursive system convolutional codes (RSC), such as low fault tolerance and high computational complexity, a novel recognition algorithm was proposed in this study. Firstly, it clearly demonstrated that the rational fraction in binary domain is capable of expanding into recurring series, and the problem of cyclic period could be solved by means of impulse response and analytical matrix. Secondly, in order to reduce the workload of computation placed on the algorithm, a polynomial database was constructed by traversing the constructed RSC code. Then, the specific matrix operation was conducted. In case of a correct ergodic polynomial, the result vector code weight tends to be significantly larger than the ergodic polynomial is incorrect, so as to realize the recognition of the polynomial. Finally, as revealed by the theoretical analysis, the fault-tolerance of the proposed algorithm was solely relevant to the code weight of the recurring series rather than the coding constraint length. The simulation results validated not only the effectiveness of the algorithm but also the correctness of the fault-tolerant performance analysis. When the error code reached as high as 0.1, the recognition rate of some polynomials was higher, and the computational complexity was lower compared to the existing algorithms.

Key words: Turbo code, component encoder, data polynomial library, recurring series, recognition