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Partial Fourier Codebooks Associated with Multiplied Golay Complementary Sequences for Compressed Sensing

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Sequences and Their Applications – SETA 2012 (SETA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7280))

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Abstract

A new (N, K) partial Fourier codebook is constructed, associated with a binary sequence obtained by an element-wise multiplication of a pair of binary Golay complementary sequences. In the codebook, N = 2m for a positive integer m, and K is approximately \(\frac{N}{4}\). It is shown that the maximum magnitude of inner products between distinct code vectors is nontrivially bounded in the codebook, which is approximately up to \(\sqrt{6}\) times the Welch bound equality for large N = 2m with odd m. Finally, the new codebook is employed as a deterministic sensing matrix for compressed sensing, where its recovery performance is tested through numerical experiments.

This work was supported by the NSERC of Canada.

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References

  1. Ailon, N., Liberty, E.: Fast dimension reduction using Rademacher series on dual BCH codes. In: Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 215–224 (2008)

    Google Scholar 

  2. Alltop, W.: Complex sequences with low periodic correlations. IEEE Trans. Inf. Theory 26(3), 350–354 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  3. Applebaum, L., Howard, S., Searle, S., Calderbank, R.: Chirp sensing codes: deterministic compressed sensing measurements for fast recovery. Appl. and Comput. Harmon. Anal. 26, 283–290 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Calderbank, R., Howard, S., Jafarpour, S.: A sublinear algorithm for sparse reconstruction with l 2/l 2 recovery guarantees. In: 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), pp. 209–212 (2009)

    Google Scholar 

  5. Calderbank, R., Howard, S., Jafarpour, S.: Construction of a large class of deterministic matrices that satisfy a statistical isometry property. IEEE J. Selected Topics in Signal Processing 4(2), 358–374 (2010)

    Article  Google Scholar 

  6. Candes, E.J., Wakin, M.B.: An introduction to compressive sampling. IEEE Sig. Proc. Mag., 21–30 (March 2008)

    Google Scholar 

  7. Davis, J.A., Jedwab, J.: Peak-to-mean power control for OFDM, Golay complementary sequences, and Reed-Muller codes. IEEE Trans. Inf. Theory 45(7), 2397–2417 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  8. DeVore, R.A.: Deterministic constructions of compressed sensing matrices. J. Complexity 28, 918–925 (2007)

    Article  MathSciNet  Google Scholar 

  9. Ding, C.: Complex codebooks from combinatorial designs. IEEE Trans. Inf. Theory 52(9), 4229–4235 (2006)

    Article  MATH  Google Scholar 

  10. Ding, C., Feng, T.: Codebooks from almost difference sets. Des. Codes Cryptogr. 46, 113–126 (2008)

    Article  MathSciNet  Google Scholar 

  11. Howard, S., Calderbank, R., Searle, S.: A fast reconstruction algorithm for deterministic compressive sensing using second order Reed-Muller codes. In: Conference on Information Sciences and Systems (CISS), Princeton, NJ, pp. 11–15 (2008)

    Google Scholar 

  12. Kovacevic, J., Chebira, A.: An introduction to frames. Foundations and Trends in Signal Processing 2(1) (2008)

    Google Scholar 

  13. MacWillams, F.J., Sloane, N.J.A.: The Theory of Error Correcting Codes. North Holland, Amsterdam (1986)

    Google Scholar 

  14. Paterson, K.G.: Generalized Reed-Muller codes and power control in OFDM modulation. IEEE Trans. Inf. Theory 46(1), 104–120 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  15. Sarwate, D.V.: Meeting the Welch bound with equality. In: Ding, C., Helleseth, T., Niederreiter, H. (eds.) Sequences and Their Applications. DMTCS Series, pp. 79–102. Springer (1999)

    Google Scholar 

  16. Sidelnikov, V.M.: Some k-valued pseudo-random sequences and nearly equidistant codes. Probl. Inf. Transm. 5, 12–16 (1969)

    MathSciNet  Google Scholar 

  17. Strohmer, T., Heath, R.: Grassmanian frames with applications to coding and communication. Appl. and Comput. Harmon. Anal. 14(3), 257–275 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  18. Tropp, J.A.: The sparsity gap: uncertainty principle proportional to dimension. In: Conference on Information Sciences and Systems (CISS), Princeton, NJ, pp. 1–6 (2010)

    Google Scholar 

  19. Tropp, J.A., Gilbert, A.C.: Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007)

    Article  MathSciNet  Google Scholar 

  20. Welch, L.R.: Lower bounds on the maximum cross correlation of signals. IEEE Trans. Inf. Theory 20(3), 397–399 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  21. Xu, Z.: Deterministic sampling of sparse trigonometric polynomials. Journal of Complexity 27(2) (2011)

    Google Scholar 

  22. Yu, N.Y.: Additive character sequences with small alphabets for compressed sensing matrices. In: IEEE Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic, pp. 2932–2935 (2011)

    Google Scholar 

  23. Yu, N.Y.: A construction of codebooks associated with binary sequences. IEEE Trans. Inf. Theory (2011) (submitted)

    Google Scholar 

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Authors and Affiliations

  1. Department of Electrical Engineering, Lakehead University, Thunder Bay, Ontario, Canada

    Xiao Bian & Nam Yul Yu

Authors
  1. Xiao Bian
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  2. Nam Yul Yu
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Editors and Affiliations

  1. Department of Informatics, University of Bergen, P.O. Box 7803, 5020, Bergen, Norway

    Tor Helleseth

  2. Department of Mathematics, Simon Fraser University, 8888 University Drive, V5A 1S6, Burnaby, BC, Canada

    Jonathan Jedwab

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Bian, X., Yu, N.Y. (2012). Partial Fourier Codebooks Associated with Multiplied Golay Complementary Sequences for Compressed Sensing. In: Helleseth, T., Jedwab, J. (eds) Sequences and Their Applications – SETA 2012. SETA 2012. Lecture Notes in Computer Science, vol 7280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30615-0_24

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  • DOI: https://doi.org/10.1007/978-3-642-30615-0_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30614-3

  • Online ISBN: 978-3-642-30615-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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