Asymptotic Formulas for Variance-Mismatched Fixed-Rate Scalar Quantization of a Gaussian Source

Asymptotic formulas are derived for the mean-squared error (MSE) distortion and the SNR of a variance-mismatched fixed-rate scalar quantizer designed MSE-optimally for a Gaussian source. It is discovered that, in the case that the standard deviation ratio ρ of the applied-to density to the designed-for density is greater than √(3/2), the SNR in dB increases at large rate
R
as 9.03
R
/ρ
²
+15(1-1/ρ
²
)log
₁₀
R
plus a constant that depends only on ρ.