Mark Goresky

Algebraic Shift Register Sequences (eBook, PDF)

• Format: PDF

Produktbeschreibung

Pseudo-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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 2. Februar 2012
• Englisch
• ISBN-13: 9781139211666
• Artikelnr.: 38278568

Autorenporträt

Mark Goresky is a member of the School of Mathematics at the Institute for Advanced Study in Princeton, New Jersey.

Inhaltsangabe

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.