[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Performance of Möbius Interleavers for Turbo Codes

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

In this paper, we study the minimum free distance and error performance of turbo encoders with Möbius interleavers. In order to be capable of estimating the minimum free distance of these interleavers using binary-fixed point (BFP) algorithm, new deterministic interleavers called “truncated Möbius interleavers” are defined and constructed. It is shown how the shifted cycles of these interleavers can be related to the cycle structure of the primary Möbius transformation and its coefficients. By adjusting some parameters, an upper bound on the number of total tested BFPs for the proposed truncated Möbius interleavers is found. One distinctive property of Möbius interleavers is that their inverse can also be represented and computed with Möbius functions. Simulations are conducted to compare the error performance of the proposed truncated Möbius interleavers with quadratic permutation polynomial (QPP) interleavers whose inverses are also representable by a quadratic equation (Ryu and Takeshita in IEEE Trans Inf Theory 52(3):1254–1260, 2006). It is finally shown that the truncated Möbius interleavers can interleave sequences of information bits faster than QPP interleavers.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Berrou, C., Glavieux, A., & Thitimajshima, P. (1993). Near Shannon limit error-correcting coding and decoding: Turbo codes. In Proceedings of international conference on communications (pp. 1064–1070).

  2. Boutros, J. J., & Zemor, G. (2006). On quasi-cyclic interleavers for parallel turbo codes. IEEE Transactions on Information Theory, 52, 1732–1739.

    Article  MathSciNet  MATH  Google Scholar 

  3. Breiling, M. (2004). A logarithmic upper bound on the minimum distance of turbo codes. IEEE Transactions on Information Theory, 50, 1692–1710.

    Article  MathSciNet  MATH  Google Scholar 

  4. Cesmelioglu, A., Meidl, W., & Topuzoglu, A. (2008). On the cycle structure of permutation polynomials. Finite Fields and Their Applications, 14(3), 593–614.

    Article  MathSciNet  MATH  Google Scholar 

  5. Corrada-Bravo, C. J., & Rubio, I. (2003). Deterministic interleavers for turbo codes with random-like performance and simple implementation. In Proceedings of 3rd international symposium on turbo codes, Brest, France.

  6. Crozier, S., & Guinand, P. (2005). Distance upper bounds and true minimum distance results for turbo codes designed with DRP interleavers. Springer Annales Des Tellecommunications, 60(1–2), 10–28.

    Google Scholar 

  7. Daneshgaran, F., & Mondin, M. (2000). Permutation fixed points with applicat-ion to estimation of minimum distance of turbo codes. IEEE Transactions on Information Theory, 46(7), 2336–2349.

    Article  MathSciNet  MATH  Google Scholar 

  8. Divsalar, D., & Pollara, F. (1995). Turbo codes for PCS applications. In Proceedings of international conference on communications, Seattle, WA.

  9. Garello, R., Pierleoni, P., & Benedetto, S. (2001). Computing the free distance of turbo codes and serially concatenated codes with interleavers: Algorithms and applications. IEEE Journal on Selected Areas in Communications, 19(5), 800–812.

    Article  Google Scholar 

  10. Hosseinalipour, S., Sakzad, A., & Sadeghi, M.-R. (2015). Minimum free distance of \(\text{CCSDS}\) turbo encoders under (truncated) Möbius interleavers. In Proceedings of 3rd Iran workshop on communication and information theory (IWCIT) 2015, Tehran, Iran (pp. 1–6).

  11. LTE; Evolved Universal Terrestrial Radio Access (E-UTRA); Multiplexing and channel coding (3GPP TS 36.212 version 8.8.0 Release 8) (2010–01). Technical specification, European Telecommunications Standards Institute (ETSI).

  12. Mullen, G. L., & Panario, D. (2013). Handbook of finite fields. Boca Raton: Chapman and Hall/CRC.

    Book  MATH  Google Scholar 

  13. Nimbalker, A., Blankenship, Y., Classon, B., & Blankenship, T. K. (2008). ARP and QPP interleavers for LTE turbo coding, wireless communications and networking conference, 2008. WCNC 2008. IEEE (pp. 1032–1037).

  14. Perotti, A., & Benedetto, S. (2004). A new upper bound on the minimum distance of turbo codes. IEEE Transactions on Information Theory, 50(12), 2985–2997.

    Article  MathSciNet  MATH  Google Scholar 

  15. Report Concerning Space Data System Standards: TM synchronization and channel coding summary of concept and rationale (2012). Informational Report CCSDS 130.1 -G-2, Green Book. Consultative Committee for Space Data Systems, Green Book.

  16. Rosnes, E. (2012). On the minimum distance of turbo codes with quadratic permutation polynomial interleavers. IEEE Transactions on Information Theory, 58(7), 4581–4795.

    Article  MathSciNet  MATH  Google Scholar 

  17. Rosnes, E., & Ytrehus, O. (2005). Improved algorithms for the determination of turbo code weight distributions. IEEE Transactions on Communications, 53(1), 20–26.

    Article  Google Scholar 

  18. Ryu, J., & Takeshita, O. Y. (2006). On quadratic inverses for quadratic permutation polynomials over integer rings. IEEE Transactions on Information Theory, 52(3), 1254–1260.

    Article  MathSciNet  MATH  Google Scholar 

  19. Sakzad, A., Sadeghi, M.-R., & Panario, D. (2012). Cycle structure of permutation functions over finite fields and their applications. Advances in Mathematics of Communications, 6(3), 347–361.

    Article  MathSciNet  MATH  Google Scholar 

  20. Sakzad, A., Panario, D., Sadeghi, M.-R., & Eshghi, N. (2010). Self-inverse interleavers based on permutation functions for turbo codes. In Proceedings of 48th annual Allerton conference on communications, control, and computing, Allerton, Chicago, USA (pp. 22–28).

  21. Sun, J., & Takeshita, O. Y. (2005). Interleavers for turbo codes using permutation polynomials over integer rings. IEEE Transactions on Information Theory, 51(1), 101–119.

    Article  MathSciNet  MATH  Google Scholar 

  22. Takeshita, O. Y. (2006). On maximum contention-free interleavers and permutation polynomials over integer rings. IEEE Transactions on Information Theory, 52(3), 1249–1253.

    Article  MathSciNet  MATH  Google Scholar 

  23. Takeshita, O. Y. (2007). Permutation polynomial interleavers: An algebraic geometric perspective. IEEE Transactions on Information Theory, 53(6), 2116–2132.

    Article  MathSciNet  MATH  Google Scholar 

  24. Takeshita, O. Y., & Costello, D. J. (2000). New deterministic interleaver designs for turbo codes. IEEE Transactions on Information Theory, 46(6), 1988–2006.

    Article  MATH  Google Scholar 

  25. Trifina, L., Munteanu, V., & Tarniceriu, D. (2009). Two methods to increase the minimum distance for turbo codes with QPP interleavers. In International symposium on signals, circuits and systems (pp. 1–4).

  26. Truhachev, D. V., Lentmaier, M., & Zigangirov, K Sh. (2001). Some results concerning design and decoding of turbo-codes. Problems of Information Transmission, 37, 190–205.

    Article  MathSciNet  MATH  Google Scholar 

  27. Vafi, S., & Wysocki, T. (2007). Weight distribution of turbo codes with convolutional interleavers. IET Communications, 1(1), 71–78.

    Article  Google Scholar 

  28. Vucetic, B., Li, Y., Perez, L. C., & Jiang, F. (2007). Recent advances in turbo code design and theory. Proceedings of the IEEE, 95(6), 1323–1344.

    Article  Google Scholar 

  29. Wicker, S. B. (1995). Error control systems for digital communications and storage. New Jersey: Prentice Hall.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran, 15914, Iran

    Seyyedali Hosseinalipour

  2. Department of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran, 15914, Iran

    Amin Sakzad & Mohammad-Reza Sadeghi

Authors
  1. Seyyedali Hosseinalipour
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amin Sakzad
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohammad-Reza Sadeghi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad-Reza Sadeghi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hosseinalipour, S., Sakzad, A. & Sadeghi, MR. Performance of Möbius Interleavers for Turbo Codes. Wireless Pers Commun 98, 271–291 (2018). https://doi.org/10.1007/s11277-017-4869-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-017-4869-9

Keywords

Search

Navigation