On Stability of Multi‐Valued Nonlinear Feedback Shift Registers

Abstract

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.

Research Status of Nonlinear Feedback Shift Register Based on Semi-Tensor Product

“…Their method for constructing reliable FSRs indicated that the number of reliable FSRs is 2 2 n −4 Φ(n) (n > 5) times of that constructed by the previous method. The methods given in [91,92] can be applied to multi-valued NFSRs, and can construct stable NFSRs. Furthermore, the literature [93,95] addressed the stability issues of (n, k) NFSR and Grain-like cascade NFSRs, respectively.…”

“…These results are helpful to the theoretical analysis of NFSRs, and have reference significance for the design of decoding algorithm. NFSRs, iteration method shown in Theorem 1 stability 2016 [85] NFSRs, reduce the computational complexity driven stability 2017 [93] (n, k) NFSRs stability 2018 [78] NFSRs with periodic input stability 2019 [91,92] multi-valued NFSRs, construct stable NFSRs stability 2020 [95] Grain-like cascade NFSRs stability 2021 [87] monotonous FSRs, construct reliable FSRs stability…”

“…These results are more novel than previous conclusions and are very helpful for the design of practical stream cipher algorithms and decoding algorithms. According to the specific research object, the main achievements can be roughly divided into the modeling of NFSRs [65][66][67], the analysis of the structure of NFSRs [68][69][70][71][72][73][74][75][76][77][78][79][80][81], and the study of the properties of NFSRs [82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97]. This paper will give an overview of the latest achievements in NFSR research based on STP from these three aspects.…”