A novel method for driven stability of NFSRs via STP.

• Convolutional code is widely used in communication systems. • NFSR is the main component of the convolutional decoder. • STP is a new mathematical tool with a wide range of applications. • NFSR can be modeled very well with STP, enabling the discussion in mathematics. The nonlinear feedback shift register (NFSR) is the main component of the convolutional decoder. This paper provides a novel method for investigating the driven stability of NFSRs with input via semi-tensor product (STP). By using the STP method, a backward state transition matrix, as well as a backward NFSR, is constructed. Backward NFSRs can help to find the predecessors of any states so that an algorithm for the global stability of autonomous NFSRs is designed. On this basis, two algorithms are proposed for the driven stability of NFSRs with input, and they have lower computational complexity than the existing methods. Meanwhile, some numerical examples are presented to support the results of this paper. Finally, the relationship between stability and connectedness is discussed fully, which derives some interesting results. [ABSTRACT FROM AUTHOR]