Skip to main content
Log in

Improved method for searching interleavers from a certain set using Garello’s method with applications for the LTE standard

  • Published:
annals of telecommunications - annales des télécommunications Aims and scope Submit manuscript

Abstract

In this paper, we propose a method for searching interleavers within a certain class, with the aim of designing turbo codes with good distance spectrum. The method is based on a modified version of Garello’s algorithm and consists in the calculation of frame error rate truncated upper bound. Here, it is applied to quadratic permutation polynomial (QPP) interleavers able to outperform those chosen for the long-term evolution (LTE) standard, for lengths up to 1,504 bits. Three classes of interleavers have been analyzed: (1) the set of QPP interleavers with the largest spread, (2) the set of QPP interleavers with a spread parameter equal to that of LTE interleaver and the highest refined nonlinearity degree, and (3) the complete set of all QPP interleavers for lengths up to 1,008. The distance spectrum optimization is made for all classes. Compared to previous methods for finding QPP-based interleavers, the search complexity is reduced, with improved performances in terms of search time, allowing interleavers of higher length. For lengths up to approximately 450, the best interleavers were found in the first class. For longer lengths, the second class contained the best ones.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /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 excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Garello R, Pierleoni P, Benedetto S (2001) Computing the free distance of turbo codes and serially concatenated codes with interleavers: algorithms and applications. IEEE J Sel Areas Commun 19(5):800–812

    Article  Google Scholar 

  2. Trifina L, Tarniceriu D, Munteanu V. Improved QPP interleavers for LTE Standard, IEEE International Symposium on Signals, Circuits and Systems (ISSCS 2011), Iasi, Romania, pp. 403–406, June 30–July 1, 2011.

  3. 3GPP TS36.212, v8.3.0 (2008–05), Multiplexing and channel coding

  4. Sun J, Takeshita OY (2005) Interleavers for turbo codes using permutation polynomial over integers rings. IEEE Trans Inf Theory 51(1):101–119

    Article  MATH  MathSciNet  Google Scholar 

  5. Takeshita OY (2006) On maximum contention-free interleavers and permutation polynomials over integers rings. IEEE Trans Inf Theory 52(3):1249–1253

    Article  MATH  MathSciNet  Google Scholar 

  6. Ryu J, Takeshita OY (2006) On quadratic inverses for quadratic permutation polynomials over integers rings. IEEE Trans Inf Theory 52(3):1254–1260

    Article  MATH  MathSciNet  Google Scholar 

  7. Takeshita OY (2007) Permutation polynomial interleavers: an algebraic–geometric perspective. IEEE Trans Inf Theory 53(6):2116–2132

    Article  MATH  MathSciNet  Google Scholar 

  8. Rosnes E, Takeshita OY (2006) Optimum distance quadratic permutation polynomial-based interleavers for turbo codes, Proc. IEEE International Symposium on Information Theory (ISIT 2006), Seattle, USA, pp. 1988–1992.

  9. Yuan J, Feng W, Vucetic B (2002) Performance of parallel and serial concatenated codes on fading channels. IEEE Trans Commun 50(10):1600–1608

    Article  Google Scholar 

  10. http://www.tlc.polito.it/garello/turbodistance/turbodistance.html

  11. Tarniceriu D, Trifina L, Munteanu V (2009) About minimum distance for QPP interleavers. Ann Telecommun 64(11–12):745–751

    Article  Google Scholar 

  12. Zhao H, Fan P, Tarokh V (2010) On the equivalence of interleavers for turbo codes using quadratic permutation polynomials over integer rings. IEEE Commun Lett 14(3):236–238

    Article  Google Scholar 

  13. Trifina L, Tarniceriu D (2013) Analysis of cubic permutation polynomials for turbo codes. Wireless Person Comm 69(1):1–22

    Google Scholar 

  14. Rosnes E (2012) On the minimum distance of turbo codes with quadratic permutation polynomial interleavers. IEEE Trans Inf Theory 58(7):4781–4795

    Article  MathSciNet  Google Scholar 

  15. Berrou C, Vaton S, Jezequel M, Douillard C (2002) Computing the minimum distance of linear codes by the error impulse method. IEEE Glob Telecommun Conf (GLOBECOM'02), Taipei Taiwan 2:1017–1020

    Google Scholar 

  16. Garello R, Vila-Casado A (2004) The all-zero iterative decoding algorithm for turbo code minimum distance computation. IEEE International Conference on Communications (ICC ‘04), Paris, France, pp.361–364

  17. Crozier S, Guinand P, Hunt A (2005) Estimating the minimum distance of turbo-codes using double and triple impulse methods. IEEE Commun Lett 9(7):631–633

    Article  Google Scholar 

  18. Crozier S, Guinand P, Hunt A (2007) Estimating the minimum distance of large-block turbo codes using iterative multiple-impulse methods. Eur Trans Telecommun 18(5):437–444

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Daniela Tarniceriu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Trifina, L., Tarniceriu, D. Improved method for searching interleavers from a certain set using Garello’s method with applications for the LTE standard. Ann. Telecommun. 69, 251–272 (2014). https://doi.org/10.1007/s12243-013-0360-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12243-013-0360-0

Keywords

Navigation