Variance-Mismatched Fixed-Rate Scalar Quantization of Laplacian Sources
Sangsin Na · IEEE Transactions on Information Theory · 2011
The paper investigates the mean-squared error (MSE) distortion of a variance-mismatched fixed-rate scalar quantizer that is optimal or asymptotically optimal in the minimum MSE sense for a Laplacian density with standard deviation σqbut is applied to another with standard deviation σp. A Nitadori-like formula is discovered for an optimal quantizer when ρ(△= σp/σq) = 1/2. Also it is shown that the distortion expressions derived rigorously for asymptotically optimal quantile quantizers essentially confirm the heuristically obtained previous result that the distortion decreases as 1/ N3/ρfor the heavy mismatch of ρ >; 3/2, as lnN/ N2for the critical mismatch of ρ = 3/2, and as 1/N2for the mild mismatch of ρ2is confirmed rigorously. In addition, optimal uniform quantizers are found to be heavily mismatched when ρ >; 1 and the resulting distortion decreases as (In N/N2)1/p.