Skip to main content
SpringerLink
Log in

Sequence Design for CDMA Systems

Mean-Square Correlation Properties of Sequence Families

  • Chapter
Difference Sets, Sequences and their Correlation Properties

Part of the book series: NATO Science Series ((ASIC,volume 542))

Abstract

Sets of sequences with “favorable” correlation properties find application in many areas including synchronization techniques, communications, and measuring systems. Depending on the application, different requirements on the correlation or other structural properties of the sequences have to be considered in the sequence design.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Barg, A. (19914) On small families of sequences with low periodic correlation, in Lecture Notes in Computer Science 781, Springer, Berlin, pp. 154–158.

    MathSciNet  Google Scholar 

  • Blake, I. and Mark, J. (1982) A note on complex sequences with low correlations, IEEE Trans. Inform. Theory 28, 814–816.

    Article  MathSciNet  MATH  Google Scholar 

  • Bortas, S., Hammons, R. and Kumar, P.V. (1992) 4-phase sequences with near-optimum correlation properties, IEEE Trans. Inform. Theory 38, 1101–1113.

    Article  Google Scholar 

  • Bortas, S. and Kumar, P.V. (1994) Binary sequences with Gold-like correlation but larger linear span, IEEE Trans. Inform. Theory 40, 532–537.

    Article  Google Scholar 

  • Calderbank, A.R. (1999) Error correcting code, correlation and quantum entanglement, this volume.

    Google Scholar 

  • Davis, J.A., Jedwab, J.A. and Paterson, K.G. (1999), Codes, correlations and power control in OFDM, this volume.

    Google Scholar 

  • Gold, R. (1967) Optimal binary sequences for spread spectrum multiplexing, IEEE Trans. Inform. Theory 13, 619–621.

    Article  MATH  Google Scholar 

  • Gold, R. (1968) Maximal recursive sequences with 3-valued periodic cross-correlation functions, IEEE Trans. Inform. Theory 14, 154–156.

    Article  MATH  Google Scholar 

  • Golomb, S.W. (1999) Construction of signals with favorable correlation properties, this volume.

    Google Scholar 

  • Hammons, A., Kumar, P.V., Calderbank, A., Sloane, N.J.A. and Solé, P. (1994) The Z4-linearity of Kerdock, Preparata, Goethals and related codes, IEEE Trans. Inform. Theory 40, 301–319.

    Article  MathSciNet  MATH  Google Scholar 

  • Helleseth, T. and Kumar, P.V. (1998) Sequences with low correlation, in V.S. Pless, W.C. Huffman (eds.), Handbook of Coding Theory, Elsevier Press.

    Google Scholar 

  • Helleseth, T. and Kumar, P.V. (1999) Codes and sequences over Z4—A tutorial overview, this volume.

    Google Scholar 

  • Kasami, T. (1969) Weight Distribution of Bose-Chaudhuri-Hocquenghem Codes, Univ. of North Carolina Press, Chapel Hill, NC.

    Google Scholar 

  • Kumar, P.V., Helleseth, T. and Calderbank, A.R. (1994) An upper bound for some exponential sums over Galois rings and applications, in Proc. Int. Symp. on Inform. Theory,Trondheim, p.70.

    Google Scholar 

  • Kumar, P.V., Helleseth, T. and Calderbank, A.R. (1995) An upper bound for Weil exponential sums over Galois rings and applications, IEEE Trans. Inform. Theory 41, 456–468.

    Article  MathSciNet  MATH  Google Scholar 

  • Kumar, P.V., Helleseth, T., Calderbank, A.R. and Hammons, A. (1996) Large families of quaternary sequences with low correlation, IEEE Trans. Inform. Theory 42, 579–592.

    Article  MathSciNet  MATH  Google Scholar 

  • Kumar, P.V. and Moreno, O. (1991) Prime-phase sequences with periodic correlation properties better than binary sequences, IEEE Trans. Inform. Theory 37, 603–616.

    Article  MATH  Google Scholar 

  • Levenshtein, V. (1998) Universal bounds for codes and designs, in W.C. Huffman, V.S.Pless (eds.), Handbook of Coding Theory, Elsevier Press.

    Google Scholar 

  • Lidl, R. and Niederreiter, H. (1983) Finite Fields, Addison-Wesley, Reading.

    MATH  Google Scholar 

  • Massey, J. and Mittelholzer, T. (1993) Welch’s Bound and sequence sets for code-division multiple-access systems, in R. Capocelli, A. De Santis and U. Vacarro (eds.), Sequences II: Methods in Communication,Security and Computer Science, Springer, Berlin, pp.63–78.

    Chapter  Google Scholar 

  • Nechaev, A. (1991) The Kerdock code in a cyclic form, Discrete Math. Appl. 1, 365–384.

    Article  MathSciNet  MATH  Google Scholar 

  • Pursley, M. (1977) Performance evaluation for phase-coded spread-spectrum multipleaccess communication — part I: System analysis, IEEE Trans. Commun. 25, 795–799.

    Article  MATH  Google Scholar 

  • Pursley, M. and Sarwate, D. (1977) Performance evaluation for phase-coded spreadspectrum multiple-access communication — part II: Code sequence analysis, IEEE Trans. Commun. 25, 800–803.

    Article  MATH  Google Scholar 

  • Rothaus, O. (1993) Modified Gold codes, IEEE Trans. Inform. Theory 39, 654–656.

    Article  MathSciNet  MATH  Google Scholar 

  • Sarwate, D. (1979) Bounds on crosscorrelation and autocorrelation of sequences, IEEE Trans. Inform. Theory 25, 720–724.

    Article  MathSciNet  MATH  Google Scholar 

  • Sarwate, D. (1983) Sets of complementary sequences, Electron. Lett. 19, 711–712.

    Article  Google Scholar 

  • Sarwate, D. (1984) Mean-square correlation of shift-register sequences, Proc. IEEE 131, 101–106.

    Google Scholar 

  • Schotten, H. (1997a) Mean-square correlation parameters of code-sequences in DS-CDMA systems, in Proc. IEEE International Symposium on Information Theory ISIT’97, Ulm, p.486.

    Google Scholar 

  • Schotten, H. (1997b) Algebraische Konstruktion gut korrelierender Sequenzen and Analyse ihrer Leistungsfähigkeit in Codemultiplex-Systemen, PhD Thesis, Aachen Univ. of Technology.

    Google Scholar 

  • Schotten, H. and Elders-Boll, H. (1998) Aperiodic mean-square correlation parameters of binary 7Z4-linear sequences, in Proc. IEEE International Symposium on Information Theory ISIT’98,Cambridge, p.402.

    Google Scholar 

  • Schotten, H., Elders-Boll, H. and Busboom, A. (1998) Optimization of spreading-sequences for DS-CDMA systems and frequency-selective fading channels, in Fifth International Symposium on Spread Spectrum Techniques and Applications ISSSTA `98, Sun City, pp.33–37.

    Google Scholar 

  • Schotten, H., Liesenfeld, B. and Elders-Boll, H. (1995) Lage families of code-sequences for direct-sequence CDMA systems, International Journal of Electronics and Communications 49, 143–150.

    Google Scholar 

  • Shanbhag, A., Kumar, P.V. and Helleseth, T. (1996) Improved binary codes and sequence families from Z4-linear codes, IEEE Trans. Inform. Theory 42, 1582–1586.

    Article  MathSciNet  MATH  Google Scholar 

  • Sidelnikov, V. (1971a) Cross-correlation of sequences, Probl. Kybern. 24, 15–42, (in russian).

    Google Scholar 

  • Sidelnikov, V. (1971b) On mutual correlation of sequences, Soviet Math. Doklady 12, 197–201.

    Google Scholar 

  • Solé, P. (1989) A quarternary cyclic code and a family of quadriphase sequences with low correlation properties, in Coding Theory and Applications, Lecture Notes in Computer Science 388, Springer, Berlin, pp. 193–201.

    Google Scholar 

  • Tarnanen, H. and Tietäväinen, A. (1994) A simple method to estimate the maximum nontrivial correlation of some sets of sequences, Appl. Algebra in Eng., Comm. and Computing 5, 123–128.

    MATH  Google Scholar 

  • Udaya, S. and Siddiqi, M.U. (1996) Optimal biphase sequences with large linear complexity derived from sequences over Z4, IEEE Trans. Inform. Theory 42, 206–216.

    Article  MathSciNet  MATH  Google Scholar 

  • Welch, L.R. (1974) Lower bounds on the maximum cross correlation of signals, IEEE Trans. Inform. Theory 20, 397–399.

    Article  MathSciNet  MATH  Google Scholar 

  • J. Wolfmann (1999), Bent functions and coding theory, this volume.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Elektrische Nachrichtentechnik, Aachen University of Technology (RWTH Aachen), Aachen, D-52056, Germany

    Hans D. Schotten

Authors
  1. Hans D. Schotten
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Otto-von-Guericke-Universität, Magdeburg, Germany

    A. Pott

  2. University of Southern California, Los Angeles, USA

    P. V. Kumar

  3. University of Bergen, Norway

    T. Helleseth

  4. University of Augsburg, Germany

    D. Jungnickel

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Schotten, H.D. (1999). Sequence Design for CDMA Systems. In: Pott, A., Kumar, P.V., Helleseth, T., Jungnickel, D. (eds) Difference Sets, Sequences and their Correlation Properties. NATO Science Series, vol 542. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4459-9_15

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-4459-9_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-5959-3

  • Online ISBN: 978-94-011-4459-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation