Fibonacci and Galois representations of feedback-with-carry shift registers

Feedback with carry shift registers (FCSRs) are a class of finite state devices that are similar to linear feedback shift registers (LFSRs) in their simplicity and statistical randomness, and in that they have algebraic tools for the analysis of their output. In this paper we describe and analyze an alternative architecture for FCSRs that is similar to the Galois architecture for LFSRs. We also explore architectural considerations for d-FCSRs, a natural generalization of FCSRs. Finally, we describe a general framework for algebraically modeling LFSRs, FCSRs, and d-FCSRs in both their Fibonacci and Galois architectures.