Mark Goresky, Andrew KlapperCambridge University Press, 2/2/2012EAN 9781107014992, ISBN10: 1107014999Hardcover, 514 pages, 24.7 x 17.4 x 3.1 cmLanguage: EnglishPseudo-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.1. IntroductionPart I. Algebraically Defined Sequences2. Sequences3. Linear feedback shift registers and linear recurrences4. Feedback with carry shift registers and multiply with carry sequences5. Algebraic feedback shift registers6. d-FCSRs7. Galois mode, linear registers, and related circuitsPart II. Pseudo-Random and Pseudo-Noise Sequences8. Measures of pseudo-randomness9. Shift and add sequences10. M-sequences11. Related sequences and their correlations12. Maximal period function field sequences13. Maximal period FCSR sequences14. Maximal period d-FCSR sequencesPart III. Register Synthesis and Security Measures15. Register synthesis and LFSR synthesis16. FCSR synthesis17. AFSR synthesis18. Average and asymptotic behavior of security measuresPart IV. Algebraic BackgroundA. Abstract algebraB. FieldsC. Finite local rings and Galois ringsD. Algebraic realizations of sequencesBibliographyIndex."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
