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On the matrix feedback shift register synthesis for matrix sequences

矩阵序列的矩阵反馈移位寄存器综合问题

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Abstract

In this paper, a generalization of the linear feedback shift register synthesis problem is presented for synthesizing minimum-length matrix feedback shift registers (MFSRs for short) to generate prescribed matrix sequences and so a new complexity measure, that is, matrix complexity, is introduced. This problem is closely related to the minimal partial realization in linear systems and so can be solved through any minimal partial realization algorithm. All minimum-length MFSRs capable of generating a given matrix sequence with finite length are characterized and a necessary and sufficient condition for the uniqueness issue is obtained. Furthermore, the asymptotic behavior of the matrix complexity profile of random vector sequences is determined.

摘要

创新点

  1. (1)

    提出并解决了矩阵序列的矩阵反馈移位寄存器综合问题;

  2. (2)

    利用对偶格的性质, 对于有限长的矩阵序列, 给出了所有生成该序列的最短的矩阵反馈移位寄存器及其唯一的充要条件。

  3. (3)

    提出了矩阵序列的矩阵复杂度并给出了向量序列的矩阵复杂度轮廓的渐进性质。

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Authors and Affiliations

  1. Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Liping Wang

  2. Zhengzhou Information Science and Technology Institute, Zhengzhou, 450002, China

    Guang Zeng

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  1. Liping Wang
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  2. Guang Zeng
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Correspondence to Liping Wang.

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Wang, L., Zeng, G. On the matrix feedback shift register synthesis for matrix sequences. Sci. China Inf. Sci. 59, 32107 (2016). https://doi.org/10.1007/s11432-015-5302-1

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  • DOI: https://doi.org/10.1007/s11432-015-5302-1

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