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Stability of nonlinear feedback shift registers


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Convolutional codes have been widely used in many applications such as digital video, radio, and mobile communication. Nonlinear feedback shift registers (NFSRs) are the main building blocks in convolutional decoders. A decoding error may result in a succession of further decoding errors. However, a stable NFSR can limit such an error-propagation. This paper studies the stability of NFSRs using a Boolean network approach. A Boolean network is an autonomous system that evolves as an automaton through Boolean functions. An NFSR can be viewed as a Boolean network. Based on its Boolean network representation, some sufficient and necessary conditions are provided for globally (locally) stable NFSRs. To determine the global stability of an NFSR with its stage greater than 1, the Boolean network approach requires lower time complexity of computations than the exhaustive search and the Lyapunov’s direct method.



卷积码广泛地应用于视频、无线电和移动通讯中。非线性反馈移位寄存器是卷积码译码器中的一个重要组件。一个译码错误可能导致一系列的译码错误。 然而,稳定的非线性反馈移位寄存器可以限制这种译码错误的扩散。 本文利用布尔网络方法研究非线性反馈移位寄存器的稳定性。 布尔网络是通过布尔函数进行演变的自动机。 非线性反馈移位寄存器可以看作是一个布尔网络。 基于它的布尔网络表示,给出了非线性反馈移位寄存器全局 (局部) 稳定的一些充分/必要条件。 对于判别级数大于1的非线性反馈移位寄存器的全局稳定性,布尔网络方法比穷举法和李雅普诺夫方法的计算复杂度更低。



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Correspondence to Jianghua Zhong.

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Zhong, J., Lin, D. Stability of nonlinear feedback shift registers. Sci. China Inf. Sci. 59, 1–12 (2016). https://doi.org/10.1007/s11432-015-5311-0

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  • nonlinear feedback shift register
  • stability
  • Boolean function
  • Boolean network
  • semi-tensor product
  • 012204


  • 非线性反馈移位寄存器
  • 稳定性
  • 布尔函数
  • 布尔网络
  • 半张量积