Skip to main content
SpringerLink
Log in
Book cover

Identification and Other Probabilistic Models pp 231–269Cite as

Common Randomness in Information Theory and Cryptography CR Capacity

  • Chapter
  • First Online:

  • 611 Accesses

Part of the book series: Foundations in Signal Processing, Communications and Networking ((SIGNAL,volume 16))

Abstract

The CR capacity of a two-terminal model is defined as the maximum rate of common randomness that the terminals can generate using resources specified by the given model. We determine CR capacity for several models, including those whose statistics depend on unknown parameters. The CR capacity is shown to be achievable robustly, by common randomness of nearly uniform distribution no matter what the unknown parameters are. Our CR capacity results are relevant for the problem of identification capacity, and also yield a new result on the regular (transmission) capacity of arbitrarily varying channels with feedback.

This is a preview of subscription content, 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   69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   89.99
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

Learn about institutional subscriptions

References

  1. R. Ahlswede, Elimination of correlation in random codes for arbitrarily varying channels. Zeitschrift Wahrscheinlichkeitstheorie und verw. Geb. 33, 159–175 (1978)

    Article  MathSciNet  Google Scholar 

  2. R. Ahlswede, A method of coding and an application to arbitrarily varying channels. J. Combin. Inf. Syst. Sci. 5, 1035 (1980)

    MathSciNet  Google Scholar 

  3. R. Ahlswede, Coloring hypergraphs: a new approach to multiuser source coding. J. Combin. Inf. Syst. Sci. 1, 76–115 (1979) and 2, 220–268 (1980)

    Google Scholar 

  4. R. Ahlswede, V.B. Balakirsky, Identification under random processes. Preprint 95–098, SFB 343, “Diskrete Strukturen in der Mathematik”, Universität Bielefeld. Problemy peredachii informatsii (special issue devoted to M.S. Pinsker), 32(1), 144–160 (1996)

    Google Scholar 

  5. R. Ahlswede, N. Cai, Z. Zhang, On interactive communication. Preprint 93–066, SFB 343 “Diskrete Strukturen in der Mathematik”, Universität Bielefeld. IEEE Trans. Inf. Theory 43(1), 22–37 (1997)

    Google Scholar 

  6. R. Ahlswede, I. Csiszár, Common randomness in information theory and cryptography, Part I: Secret sharing. IEEE Trans. Inf. Theory 39, 1121–1132 (1993)

    MathSciNet  MATH  Google Scholar 

  7. R. Ahlswede, I. Csiszár, Common randomness in information theory and cryptography, Part II: CR capacity. IEEE Trans. Inf. Theory 44(1), 225–240 (1998)

    MATH  Google Scholar 

  8. R. Ahlswede, G. Dueck, Identification via channels. IEEE Trans. Inf. Theory 35, 15–29 (1989)

    Article  MathSciNet  Google Scholar 

  9. R. Ahlswede, G. Dueck, Identification in the presence of feedback – a discovery of new capacity formulas. IEEE Trans. Inf. Theory 35, 30–39 (1989)

    Article  MathSciNet  Google Scholar 

  10. R. Ahlswede, B. Verboven, On identification via multi-way channels with feedback. IEEE Trans. Inf. Theory 37, 1519–1526 (1991)

    Article  Google Scholar 

  11. R. Ahlswede, Z. Zhang, New directions in the theory of identification via channels. Preprint 94–010, SFB 343 “Diskrete Strukturen in der Mathematik”, Universität Bielefeld. IEEE Trans. Inf. Theory 41(4), 1040–1050 (1995)

    Google Scholar 

  12. D. Blackwell, L. Breiman, A.J. Thomasian, The capacities of certain channel classes under random coding. Ann. Math. Stat. 31, 558–567 (1960)

    Article  Google Scholar 

  13. I. Csiszár, J. Körner, On the capacity of the arbitrarily varying channels for maximum probability of error. Z. Wahrscheinlichkeitsth. Verw. Gebiete 57, 87–101 (1981)

    Article  MathSciNet  Google Scholar 

  14. I. Csiszár, J. Körner, Information Theory: Coding Theorem for Discrete Memoryless Systems (Academic, New York, 1982)

    MATH  Google Scholar 

  15. I. Csiszár, P. Narayan, The capacity of the arbitrarily varying channel revisited: positivity, constraints. IEEE Trans. Inf. Theory 34, 181–193 (1988)

    Article  MathSciNet  Google Scholar 

  16. I. Csiszár, P. Narayan, Capacity of the Gaussian arbitrarily varying channel. IEEE Trans. Inf. Theory 37, 18–26 (1991)

    Article  MathSciNet  Google Scholar 

  17. P. Gács, J. Körner, Common information is far less than mutual information. Probl. Control Inf. Theory 21, 149–162 (1973)

    MathSciNet  MATH  Google Scholar 

  18. J. Kiefer, J. Wolfowitz, Channels with arbitrarily varying channel probability functions. Inf. Control 5, 44–54 (1962)

    Article  MathSciNet  Google Scholar 

  19. M. Salehi, Cardinality bounds on auxiliary variables in multiple–user theory via the method of Ahlswede and Körner, Stanford Technical Report (1978)

    Google Scholar 

  20. D. Slepian, J.K. Wolf, Noiseless coding of correlated information sources. IEEE Trans. Inf. Theory 19, 471–480 (1973)

    Article  MathSciNet  Google Scholar 

  21. S. Venkatesan, V. Anantharam, The common randomness capacity of independent discrete memoryless channels, Memorandum No. UCB/ERL M95/85 (1995)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bielefeld, Germany

    Rudolf Ahlswede

Authors
  1. Rudolf Ahlswede
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Bielefeld, Germany

    Alexander Ahlswede

  2. Faculty Mathematics and Computer Science, Friedrich-Schiller-University Jena, Jena, Germany

    Ingo Althöfer

  3. Institute for Communications Engineering, Technical University of Munich, München, Germany

    Christian Deppe

  4. Fachbereich Wirtschaft und Gesundheit, Fachhochschule Bielefeld, Bielefeld, Germany

    Ulrich Tamm

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Ahlswede, R. (2021). Common Randomness in Information Theory and Cryptography CR Capacity. In: Ahlswede, A., Althöfer, I., Deppe, C., Tamm, U. (eds) Identification and Other Probabilistic Models. Foundations in Signal Processing, Communications and Networking, vol 16. Springer, Cham. https://doi.org/10.1007/978-3-030-65072-8_15

Download citation

Publish with us

Policies and ethics

Search

Navigation