Stability of nonlinear feedback shift registers

Convolutional code are widely used in many applications such as digital video, radio, and mobile communication. Nonlinear feedback shift registers (NFSRs) are the main building blocks in many convolutional decoders. A decoding error may result in a successive 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, the Boolean network approach requires lower time complexity than the exhaustive search and the Lyapunov's direct method.