Skip to main content

Abstract

We give an explicit construction of a function that is almost a 2-source extractor for linear entropy, it is a condenser where the output has almost full entropy. Given 2 sources with entropy δn, the output of the condenser is a distribution on m-bit strings that is -close to having min-entropy , where here m is linear in n.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

  1. Barak, B., Kindler, G., Shaltiel, R., Sudakov, B., Wigderson, A.: Simulating independence: New constructions of condensers, Ramsey graphs, dispersers, and extractors. In: Proceedings of the 37th Annual ACM Symposium on Theory of Computing, pp. 1–10 (2005)

    Google Scholar 

  2. Barak, B., Rao, A., Shaltiel, R., Wigderson, A.: 2 source dispersers for n o(1) entropy and Ramsey graphs beating the Frankl-Wilson construction. In: Proceedings of the 38th Annual ACM Symposium on Theory of Computing (2006)

    Google Scholar 

  3. Bourgain, J.: More on the sum-product phenomenon in prime fields and its applications. International Journal of Number Theory 1, 1–32 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bourgain, J., Katz, N., Tao, T.: A sum-product estimate in finite fields, and applications. Geometric and Functional Analysis 14, 27–57 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chor, B., Goldreich, O.: Unbiased bits from sources of weak randomness and probabilistic communication complexity. SIAM Journal on Computing 17(2), 230–261 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  6. Dvir, Z., Raz, R.: Analyzing linear mergers. Technical Report TR05-25, ECCC: Electronic Colloquium on Computational Complexity (2005)

    Google Scholar 

  7. Gabizon, A., Raz, R., Shaltiel, R.: Deterministic extractors for bit-fixing sources by obtaining an independent seed. In: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science (2004)

    Google Scholar 

  8. Guruswami, V., Umans, C., Vadhan, S.: Unbalanced expanders and randomness extractors from parvaresh-vardy codes. In: Proceedings of the 22nd Annual IEEE Conference on Computational Complexity (2007)

    Google Scholar 

  9. Lu, C.J., Reingold, O., Vadhan, S., Wigderson, A.: Extractors: Optimal up to constant factors. In: Proceedings of the 35th Annual ACM Symposium on Theory of Computing, pp. 602–611 (2003)

    Google Scholar 

  10. Nisan, N., Zuckerman, D.: Randomness is linear in space. Journal of Computer and System Sciences 52(1), 43–52 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  11. Rao, A.: Extractors for a constant number of polynomially small min-entropy independent sources. In: Proceedings of the 38th Annual ACM Symposium on Theory of Computing (2006)

    Google Scholar 

  12. Raz, R.: Extractors with weak random seeds. In: Proceedings of the 37th Annual ACM Symposium on Theory of Computing, pp. 11–20 (2005)

    Google Scholar 

  13. Santha, M., Vazirani, U.V.: Generating quasi-random sequences from semi-random sources. Journal of Computer and System Sciences 33, 75–87 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  14. Shaltiel, R.: How to get more mileage from randomness extractors. In: Proceedings of the 21th Annual IEEE Conference on Computational Complexity, pp. 49–60 (2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Ashish Goel Klaus Jansen José D. P. Rolim Ronitt Rubinfeld

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Rao, A. (2008). A 2-Source Almost-Extractor for Linear Entropy. In: Goel, A., Jansen, K., Rolim, J.D.P., Rubinfeld, R. (eds) Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2008 2008. Lecture Notes in Computer Science, vol 5171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85363-3_43

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-85363-3_43

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85362-6

  • Online ISBN: 978-3-540-85363-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics