Skip to main content
SpringerLink
Log in

A Survey of Results for Deletion Channels and Related Synchronization Channels

  • Conference paper
Algorithm Theory – SWAT 2008 (SWAT 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5124))

Included in the following conference series:

Abstract

The binary symmetric channel, where each bit is independently received in error with probability p, and the binary erasure channel, where each bit is erased with probability p, enjoy a long and rich history. Shannon developed the fundamental results on the capacity of such channels in the 1940’s [19], and in recent years, through the development and analysis of low-density parity-check codes and related families of codes, we understand how to achieve near-capacity performance for such channels extremely efficiently [2,13,17].

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 99.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.00
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

References

  1. Batu, T., Kannan, S., Khanna, S., McGregor, A.: Reconstructing strings from random traces. In: Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 910–918 (2004)

    Google Scholar 

  2. Chung, S.Y., Forney Jr., G.D., Richardson, T.J., Urbanke, R.: On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit. IEEE Communications Letters 5(2), 58–60 (2001)

    Article  Google Scholar 

  3. Davey, M.C., Mackay, D.J.C.: Reliable communication over channels with insertions, deletions, and substitutions. IEEE Transactions on Information Theory 47(2), 687–698 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Diggavi, S., Grossglauser, M.: On information transmission over a finite buffer channel. IEEE Transactions on Information Theory 52(3), 1226–1237 (2006)

    Article  MathSciNet  Google Scholar 

  5. Diggavi, S., Mitzenmacher, M., Pfister, H.: Capacity upper bounds for deletion channels. In: Proceedings of the 2007 IEEE International Symposium on Information Theory (ISIT), pp. 1716–1720 (2007)

    Google Scholar 

  6. Drinea, E., Kirsch, A.: Directly lower bounding the information capacity for channels with i.i.d. deletions and duplications. In: Proceedings of the 2007 IEEE International Symposium on Information Theory (ISIT), pp. 1731–1735 (2007)

    Google Scholar 

  7. Drinea, E., Mitzenmacher, M.: On lower bounds for the capacity of deletion channels. IEEE Transactions on Information Theory 52(10), 4648–4657 (2006)

    Article  MathSciNet  Google Scholar 

  8. Drinea, E., Mitzenmacher, M.: Improved lower bounds for the capacity of i.i.d. deletion and duplication channels. IEEE Transactions on Information Theory 53(8), 2693–2714 (2007)

    Article  MathSciNet  Google Scholar 

  9. Holenstein, T., Mitzenmacher, M., Panigrahy, R., Wieder, U.: Trace reconstruction with constant deletion probability and related results. In: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 389–398 (2008)

    Google Scholar 

  10. Levenshtein, V.I.: Binary codes capable of correcting deletions, insertions, and reversals. Soviet Phys. -Dokl 10(8), 707–710 (1966), (English translation)

    MathSciNet  Google Scholar 

  11. Levenshtein, V.I.: Efficient reconstruction of sequences. IEEE Transactions on Information Theory 47(1), 2–22 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Liu, Z., Mitzenmacher, M.: Codes for deletion and insertion channels with segmented errors. In: Proceedings of the 2007 IEEE International Symposium on Information Theory (ISIT), pp. 846–850 (2007)

    Google Scholar 

  13. Luby, M.G., Mitzenmacher, M., Shokrollahi, M.A., Spielman, D.A.: Efficient erasure correcting codes. IEEE Transactions on Information Theory 47(2), 569–584 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  14. Mitzenmacher, M.: Polynomial time low-density parity-check codes with rates very close to the capacity of the q-ary random deletion channel for large q. IEEE Transactions on Information Theory 52(12), 5496–5501 (2006)

    Article  MathSciNet  Google Scholar 

  15. Mitzenmacher, M.: Capacity bounds for sticky channels. IEEE Transactions on Information Theory 54(1), 72 (2008)

    Article  MathSciNet  Google Scholar 

  16. Mitzenmacher, M., Drinea, E.: A simple lower bound for the capacity of the deletion channel. IEEE Transactions on Information Theory 52(10), 4657–4660 (2006)

    Article  MathSciNet  Google Scholar 

  17. Richardson, T.J., Shokrollahi, M.A., Urbanke, R.L.: Design of capacity-approaching irregular low-density parity-check codes. IEEE Transactions on Information Theory 47(2), 619–637 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  18. Schulman, L.J., Zuckerman, D.: Asymptotically good codes correcting insertions, deletions, and transpositions. IEEE Transactions on Information Theory 45(7), 2552–2557 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  19. Shannon, C.E.: A mathematical theory of communication. Bell Systems Technical Journal 27(3), 379–423 (1948)

    MathSciNet  Google Scholar 

  20. Sloane, N.J.A.: On single-deletion-correcting codes. Codes and Designs. In: Proceedings of a Conference Honoring Professor Dijen K. Ray-Chaudhuri on the Occasion of His 65th Birthday, Ohio State University, May 18-21, 2000 (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Engineering and Applied Sciences, Harvard University,  

    Michael Mitzenmacher

Authors
  1. Michael Mitzenmacher
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Joachim Gudmundsson

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mitzenmacher, M. (2008). A Survey of Results for Deletion Channels and Related Synchronization Channels. In: Gudmundsson, J. (eds) Algorithm Theory – SWAT 2008. SWAT 2008. Lecture Notes in Computer Science, vol 5124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69903-3_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-69903-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69900-2

  • Online ISBN: 978-3-540-69903-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation