The Journal of Korean Institute of Communications and Information Sciences (한국통신학회논문지)

The Korean Institute of Commucations and Information Sciences (한국통신학회)
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Signal-to-Noise Ratio Formulas of a Scalar Gaussian Quantizer Mismatched to a Laplacian Source

  • Rhee, Ja-Gan (Department of Electrical and Computer Engineering, Ajou University) ;
  • Na, Sang-Sin (Department of Electrical and Computer Engineering, Ajou University)
  • Received : 2011.03.05
  • Accepted : 2011.05.11
  • Published : 2011.06.30
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Abstract

The paper derives formulas for the mean-squared error distortion and resulting signal-to-noise (SNR) ratio of a fixed-rate scalar quantizer designed optimally in the minimum mean-squared error sense for a Gaussian density with the standard deviation ${\sigma}_q$ when it is mismatched to a Laplacian density with the standard deviation ${\sigma}_q$. The SNR formulas, based on the key parameter and Bennett's integral, are found accurate for a wide range of $p\({\equiv}\frac{\sigma_p}{\sigma_q}\){\geqq}0.25$. Also an upper bound to the SNR is derived, which becomes tighter with increasing rate R and indicates that the SNR behaves asymptotically as $\frac{20\sqrt{3{\ln}2}}{{\rho}{\ln}10}\;{\sqrt{R}}$ dB.

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References

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