Algebraic Shift Register Sequences
Algebraic Shift Register Sequences
Andrew Klapper, University of Kentucky
$121.00
USDPseudo-random sequences are essential ingredients of every modern digital communication system including cellular telephones, GPS, secure internet transactions and satellite imagery. Each application requires pseudo-random sequences with specific statistical properties. This book describes the design, mathematical analysis and implementation of pseudo-random sequences, particularly those generated by shift registers and related architectures such as feedback-with-carry shift registers. The earlier chapters may be used as a textbook in an advanced undergraduate mathematics course or a graduate electrical engineering course; the more advanced chapters provide a reference work for researchers in the field. Background material from algebra, beginning with elementary group theory, is provided in an appendix.
- Self-contained chapters make the book accessible to a wide range of students
- Complete proofs are provided and exercises are included in chapters covering basic material
- Provides a unified approach to a wide range of pseudo-random sequences
Reviews & endorsements
"This book is a welcome addition to the personal library of anyone interested in pseudo-random sequences. It is, undoubtedly, a very serious monograph on this subject, which attempts to unify many types of sequence generators, using algebraic methods. The book is the fruit of a longtime collaboration on algebraic shift registers between its two authors. All in all, the book is rigorous but accessible and pleasantly written."
Pantelimon Stanica, Mathematical Reviews
"This elegant text casts highly practical mathematics as replete with miraculous theoretical novelties. It thus serves specialists while simultaneously envincing a broad appeal. Recommended."
D.V. Feldman, Choice magazine
Product details
June 2012Adobe eBook Reader
9781139211666
0 pages
0kg
35 b/w illus. 35 tables 90 exercises
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- 1. Introduction
- Part I. Algebraically Defined Sequences:
- 2. Sequences
- 3. Linear feedback shift registers and linear recurrences
- 4. Feedback with carry shift registers and multiply with carry sequences
- 5. Algebraic feedback shift registers
- 6. d-FCSRs
- 7. Galois mode, linear registers, and related circuits
- Part II. Pseudo-Random and Pseudo-Noise Sequences:
- 8. Measures of pseudo-randomness
- 9. Shift and add sequences
- 10. M-sequences
- 11. Related sequences and their correlations
- 12. Maximal period function field sequences
- 13. Maximal period FCSR sequences
- 14. Maximal period d-FCSR sequences
- Part III. Register Synthesis and Security Measures:
- 15. Register synthesis and LFSR synthesis
- 16. FCSR synthesis
- 17. AFSR synthesis
- 18. Average and asymptotic behavior of security measures
- Part IV. Algebraic Background: A. Abstract algebra
- B. Fields
- C. Finite local rings and Galois rings
- D. Algebraic realizations of sequences
- Bibliography
- Index.
