Fibonacci Representations of Linear Feedback Shift Registers and its application for spread-spectrum system

Hossein Naraghi1, M.M Motamedi-nezhad2and Hassan Naraghi3

1Department of Mathematics, PayameNoor University, P. O. Box: 19395-3697, Tehran, Iran. Email:

2Department of Mathematics, University of Applied Science and Technology, Tehran, Iran. Email:

3 Department of Electrical Engineering, Ashtian Branch, Islamic Azad University, Ashtian, Iran. Email:



A Linear Feedback Shift Registers (LFSR) with “Fibonacci” architecture is a shift register provided with a small amount of memory which is used in the feedback algorithm [l]. Like linear feedback shift registers (LFSRs), FCSRs provide a simple and predictable method for the fast generation of pseudorandom sequences with good statistical properties and large periods. In this paper, we analyze an alternative architecture for LFSRs with “Fibonacci” architecture. We use Fibonacci sequences for BPSK and we determine n-state Markov chain entropy rate.

Keywords: BPSK, Direct-sequence, Entropy, Fibonacci mode, LFSR, Markov chain, Spread-spectrum.





International eJournal of Mathematics and Engineering
7, Issue
1, Pages:  7 - 16