On Stability of Multi‐Valued Nonlinear Feedback Shift Registers
Haiyan Wang, Qiuzhen Lin, Jianyong Chen, Jianqiang Li, Jianghua Zhong, Dongdai Lin, Jia Wang, Lijia Ma · Complexity · 2019
Nonlinear feedback shift registers (NFSRs) are the main building blocks in many convolutional decoders, and a stable NFSR can limit decoding error propagation. Due to lack of efficient algebraic tools, the stability of multi‐valued NFSRs has been much less studied. This paper studies the stability of multi‐valued NFSRs using a logic network approach. A multi‐valued NFSR can be viewed as a logic network. Based on its logic network representation, some sufficient and necessary conditions are provided for globally (locally) stable multi‐valued NFSRs, explicit forms are given for the set of basins, and the algorithm for obtaining the set of basins is provided as well. Finally, a new method is presented for constructing stable n + 1‐stage NFSRs from stable n‐stage NFSRs by the properties of D‐morphism.