The Lambert W Function in the Design of Minimum Mean Square-Error Quantizers ofr a Laplacian Source 


Vol. 27,  No. 6, pp. 524-532, Jun.  2002


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  Abstract

This paper reports that the Lambert W function applies to a non-iterative design of minimum mean square-error scalar quantizers for a Laplacian source. Specifically, it considers a non-iterative design algorithm for optimum quantizers for a Laplacian source; it finds that the solution of the recursive nonlinear equation in the non-iterative design is elegantly expressed in term of the principal branch of the Lambert W function in a closed form; and it proves that the non-iterative algorithm applies only to exponential or Laplacian sources. The contribution of the paper is in the reduction of the time needed for the design and the increased accuracy in resulting quantization points and thresholds, because the algorithm is non-iterative and the Lambert W function can be evaluated as accurately as desired. Also, numerical results show how optimal quantization distortion converges monotonically to the Panter-Dite constant and help derive an approximation formula for the key parameters of optimum quantizers.

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  Cite this article

[IEEE Style]

H. Song and S. Na, "The Lambert W Function in the Design of Minimum Mean Square-Error Quantizers ofr a Laplacian Source," The Journal of Korean Institute of Communications and Information Sciences, vol. 27, no. 6, pp. 524-532, 2002. DOI: .

[ACM Style]

Hyun-jung Song and Sangsin Na. 2002. The Lambert W Function in the Design of Minimum Mean Square-Error Quantizers ofr a Laplacian Source. The Journal of Korean Institute of Communications and Information Sciences, 27, 6, (2002), 524-532. DOI: .

[KICS Style]

Hyun-jung Song and Sangsin Na, "The Lambert W Function in the Design of Minimum Mean Square-Error Quantizers ofr a Laplacian Source," The Journal of Korean Institute of Communications and Information Sciences, vol. 27, no. 6, pp. 524-532, 6. 2002.

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pISSN : 1226 - 4717
eISSN : 2287 - 3880