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Using Geometrical Properties for Fast Indexation of Gaussian Vector Quantizers

EURASIP Journal on Advances in Signal Processing volume 2007, Article number: 063192 (2006) Cite this article

Abstract

Vector quantization is a classical method used in mobile communications. Each sequence of samples of the discretized vocal signal is associated to the closest -dimensional codevector of a given set called codebook. Only the binary indices of these codevectors (the codewords) are transmitted over the channel. Since channels are generally noisy, the codewords received are often slightly different from the codewords sent. In order to minimize the distortion of the original signal due to this noisy transmission, codevectors indexed by one-bit different codewords should have a small mutual Euclidean distance. This paper is devoted to this problem of index assignment of binary codewords to the codevectors. When the vector quantizer has a Gaussian structure, we show that a fast index assignment algorithm based on simple geometrical and combinatorial considerations can improve the SNR at the receiver by 5dB with respect to a purely random assignment. We also show that in the Gaussian case this algorithm outperforms the classical combinatorial approach in the field.

References

  1. Gray RM: Vector quantization. IEEE Acoustics, Speech, and Signal Processing Magazine 1984,1(2):4–29.

    Google Scholar 

  2. Makhoul J, Roucos S, Gish H: Vector quantization in speech coding. Proceedings of the IEEE 1985,73(11):1551–1588.

    Article  Google Scholar 

  3. Schroeder MR, Atal BS: Code-excited linear prediction (CELP): high-quality speech at very low bit rates. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '85), April 1985, Tampa, Fla, USA 10: 937–940.

    Article  Google Scholar 

  4. Gao Y, Benyassine A, Thyssen J, Su H, Shlomot E: eX-CELP: a speech coding paradigm. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '01), May 2001, Salt Lake City, Utah, USA 2: 689–692.

    Google Scholar 

  5. Gao Y, Shlomot E, Benyassine A, Thyssen J, Su H, Murgia C: The SMV algorithm selected by TIA and 3GPP2 for CDMA applications. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '01), May 2001, Salt Lake City, Utah, USA 2: 709–712.

    Google Scholar 

  6. Makinen J, Ojala P, Toukomaa H: Performance comparison of source controlled GSM AMR and SMV vocoders. Proceedings of International Symposium on Intelligent Signal Processing and Communications Systems (ISPACS '04), November 2004, Seoul, Korea 151–154.

    Google Scholar 

  7. De Marca JRB, Jayant NS: An algorithm for assigning binary indices to the codevectors of a multi-dimensional quantizer. Proceedings of IEEE International Conference on Communications, 1987, Seattle, Wash, USA 1128–1132.

    Google Scholar 

  8. Freeman JA, Skapura DM: Neural Networks—Algorithms, Applications and Programming Techniques. Addison Wesley, Reading, Mass, USA; 1992.

    MATH  Google Scholar 

  9. Hagen R, Hedelin P: Robust vector quantization in spectral coding. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '93), April 1993, Minneapolis, Minn, USA 2: 13–16.

    Google Scholar 

  10. Knagenhjelm P: How good is your index assignment? Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '93), April 1993, Minneapolis, Minn, USA 2: 423–426.

    Google Scholar 

  11. Knagenhjelm P, Agrell E: The hadamard transform—a tool for index assignment. IEEE Transactions on Information Theory 1996,42(4):1139–1151. 10.1109/18.508837

    Article  Google Scholar 

  12. Zeger K, Gersho A: Pseudo-Gray coding. IEEE Transactions on Communications 1990,38(12):2147–2158. 10.1109/26.64657

    Article  Google Scholar 

  13. Cheng N-J, Kingsbury NK: Robust zero-redundancy vector quantization for noisy channels. Proceedings of IEEE International Conference on Communications (ICC '89), June 1989, Boston, Mass, USA 3: 1338–1342.

    Google Scholar 

  14. Wu H-S, Barba J: Index allocation in vector quantisation for noisy channels. Electronics Letters 1993,29(15):1317–1319. 10.1049/el:19930883

    Article  Google Scholar 

  15. Linde Y, Buzo A, Gray RM: An algorithm for vector quantizer design. IEEE Transactions on Communications Systems 1980,28(1):84–95. 10.1109/TCOM.1980.1094577

    Article  Google Scholar 

  16. Hagen R, Hedelin P: Robust vector quantization by a linear mapping of a block code. IEEE Transactions on Information Theory 1999,45(1):200–218. 10.1109/18.746788

    Article  MathSciNet  Google Scholar 

  17. Totty R, Clark G Jr.: Reconstruction error in waveform transmission. IEEE Transactions on Information Theory 1967,13(2):336–338.

    Article  Google Scholar 

  18. Potter LC, Chiang D-M: Minimax nonredundant channel coding. IEEE Transactions on Communications 1995,43(234):804–811.

    Article  Google Scholar 

  19. Chen J-H, Davidson G, Gersho A, Zeger K: Speech coding for the mobile satellite experiment. Proceedings of IEEE International Conference on Communications, 1987, Seattle, Wash, USA 756–763.

    Google Scholar 

  20. Farvardin N: A study of vector quantization for noisy channels. IEEE Transactions on Information Theory 1990,36(4):799–809. 10.1109/18.53739

    Article  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Laboratoire d'Informatique de l'Ecole Polytechnique (LIX), Ecole Polytechnique, Palaiseau Cedex, 91128, France

    E. A. Vassilieva, D. Krob & J. M. Steyaert

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  1. E. A. Vassilieva
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  2. D. Krob
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  3. J. M. Steyaert
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Correspondence to E. A. Vassilieva.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Vassilieva, E.A., Krob, D. & Steyaert, J.M. Using Geometrical Properties for Fast Indexation of Gaussian Vector Quantizers. EURASIP J. Adv. Signal Process. 2007, 063192 (2006). https://doi.org/10.1155/2007/63192

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  • DOI: https://doi.org/10.1155/2007/63192

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