Algebraic shift register sequences

著者

書誌事項

Algebraic shift register sequences

Mark Goresky, Andrew Klapper

Cambridge University Press, 2012

  • : hardback

大学図書館所蔵 件 / 全8件

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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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