Relating the cyclic behavior of linear and intrainverted feedback shift registers

Feedback shift registers (FSRs) are sometimes implemented with inversions between stages to improve their testability and their ability to locate faults. These intrainverted FSRs (IFSRs) can be realized with less overhead than standard linear feedback shift registers (LFSRs). It is shown how to relate the cyclic behavior of the LFSR and the corresponding IFSR, based on the same feedback polynomial, so that IFSRs can be designed to exploit the inherent implementation advantages while exhibiting the well-known behavior of LFSRs. In particular, it is shown that the cyclic and serial output behavior of LFSRs can be emulated by IFSRs when loaded with the appropriate initial states for most feedback shift register lengths and feedback polynomials. How the initial state for the IFSR can be derived, given the feedback polynomial and the initial state of the desired cycle in the LFSR, is described. Conditions under which such mapping of behavior cannot be guaranteed are given