Algebraic shift register sequences
著者
書誌事項
Algebraic shift register sequences
Cambridge University Press, 2012
- : hardback
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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.
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