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Methods to Search Permutation Polynomial Interleavers for Turbo Codes

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Permutation Polynomial Interleavers for Turbo Codes

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Abstract

In this chapter we present some methods to find good PP-based interleavers for turbo codes in a reasonable time. Spread factor and refined non-linearity degree metrics proposed for this goal by Takeshita (2007) are presented in Sects. 7.2 and 7.3, respectively. In Sects. 7.4 and 7.5 we present some methods to search PP interleavers adapted to a specific component code of the turbo code. These methods use both the distance spectrum of the turbo code and the metrics proposed in Takeshita (2007).

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References

  • 2001, http://www.tlc.polito.it/garello/turbodistance/turbodistance.html

  • 2015, http://telecom.etti.tuiasi.ro/tti/papers/Text_files/Number_of_true_diff_LPPs_QPPs_CPPs_N_000002_100000.txt

  • E. Boutillon, D. Gnaedig, Maximum spread of D-dimensional multiple turbo codes. IEEE Trans. Commun. 53(8), 1237–1242 (2005)

    Article  Google Scholar 

  • M. Breiling, A logarithmic upper bound on the minimum distance of turbo codes. IEEE Trans. Inf. Theory 50(8), 1692–1710 (2004)

    Article  MathSciNet  Google Scholar 

  • S. Crozier, New high-spread high-distance interleavers for turbo-codes, in 20th Bienn Symposium on Communications, Kingston, Ontario, Canada, 28–31 May 2000, pp. 3–7

    Google Scholar 

  • S. Crozier, P. Guinand, High-performance low-memory interleaver banks for turbo-codes, in IEEE 54th Vehicular Technology Conference (VTC), Atlantic City, NJ, USA, vol. 4, 7–11 October 2001, pp. 2394–2398

    Google Scholar 

  • D. Divsalar, F. Pollara, Turbo codes for PCS applications, in IEEE International Conference on Communications (ICC), Seattle, WA, USA, 18–22 June 1995, pp. 54–59

    Google Scholar 

  • S. Dolinar, D. Divsalar, Weight distribution of turbo codes using random and nonrandom permutations. TDA Progress Report (Jet Propulsion Laboratory, Pasadena, CA), 15 August 1995, pp. 42–122

    Google Scholar 

  • G.D. Forney Jr., Geometrically uniform codes. IEEE Trans. Inf. Theory 37(5), 1241–1260 (1991)

    Article  MathSciNet  Google Scholar 

  • R. Garello, P. Pierleoni, S. Benedetto, 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 (2001)

    Article  Google Scholar 

  • G.H. Hardy, E.M. Wright, An Introduction to the Theory of Numbers, 4th edn. (Oxford University Press, Oxford, 1975)

    Google Scholar 

  • C. Heegard, S.B. Wicker, Turbo Coding (Kluwer Academic Publishers, Dordrecht, 1999)

    Book  Google Scholar 

  • C.Y. Lee, Some properties of nonbinary error-correcting codes. IRE Trans. Inf. Theory 4(2), 77–82 (1958)

    Article  MathSciNet  Google Scholar 

  • A. Perotti, S. Benedetto, A new upper bound on the minimum distance of turbo codes. IEEE Trans. Inf. Theory 50(12), 2985–2997 (2004)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • O.Y. Takeshita, Permutation polynomial interleavers: an algebraic- geometric perspective. IEEE Trans. Inf. Theory 53(6), 2116–2132 (2007)

    Article  MathSciNet  Google Scholar 

  • O.Y. Takeshita, D.J. Costello Jr., New deterministic interleaver designs for turbo codes. IEEE Trans. Inf. Theory 46(6), 1988–2006 (2000)

    Article  Google Scholar 

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

    Article  Google Scholar 

  • L. Trifina, D. Tarniceriu, Analysis of cubic permutation polynomials for turbo codes. Wirel. Pers. Commun. 69(1), 1–22 (2013)

    Article  Google Scholar 

  • L. Trifina, D. Tarniceriu, Improved method for searching interleavers from a certain set using Garello’s method with applications for the LTE standard. Ann. Telecommun. 69(5–6), 251–272 (2014)

    Article  Google Scholar 

  • L. Trifina, D. Tarniceriu, On the equivalence of cubic permutation polynomial and ARP interleavers for turbo codes. IEEE Trans. Commun. 65(2), 473–485 (2017)

    Article  Google Scholar 

  • L. Trifina, V. Munteanu, H. Balta, New types of interleavers based on the Welch-Costas permutation, in Second European Conference on the Use of Modern Information and Communication Technologies (ECUMICT), Gent, Belgium, 30–31 March 2006a, pp. 107–117

    Google Scholar 

  • L. Trifina, V. Munteanu, D. Tarniceriu, Welch-Costas interleaver with cyclic shifts on groups of elements. Electron. Lett. 42(24), 1413–1415 (2006b)

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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Correspondence to Lucian Trifina .

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Trifina, L., Tarniceriu, D. (2019). Methods to Search Permutation Polynomial Interleavers for Turbo Codes. In: Permutation Polynomial Interleavers for Turbo Codes. Signals and Communication Technology. Springer, Singapore. https://doi.org/10.1007/978-981-13-2625-7_7

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  • DOI: https://doi.org/10.1007/978-981-13-2625-7_7

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  • Print ISBN: 978-981-13-2624-0

  • Online ISBN: 978-981-13-2625-7

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