Open AccessPeriods on the Cascade Connection of an LFSR and an NFSR
Author(s) -
Yang Yinghua,
Zeng Xiangyong,
Xu Yunge
Publication year - 2019
Publication title -
chinese journal of electronics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.267
H-Index - 25
eISSN - 2075-5597
pISSN - 1022-4653
DOI - 10.1049/cje.2019.01.018
Subject(s) - cascade , linear feedback shift register , connection (principal bundle) , shift register , mathematics , period (music) , stage (stratigraphy) , arithmetic , computer science , physics , chemistry , biology , telecommunications , geometry , chip , paleontology , chromatography , acoustics
We study the periods of sequences produced by the cascade connection of two Feedback shift registers (FSRs). The period of the cascade connection is the period of the longest sequences it produces. An upper bound for the period of the cascade connection of a Nonlinear feedback shift register (NFSR) into a Linear feedback shift register (LFSR) is established. In addition, the cascade connection of an n ‐stage maximum‐length LFSR into an n‐stage NFSR is called an ( n + n )‐stage Grain‐like NFSR, and we propose two families of ( n + n )stage Grain‐like NFSRs such that the minimal period 2 n ‐ 1 is achievable for a positive integer n .