Asymptotically efficient quantizing

By Herbert Gish, J. Pierce. 1968

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Citations in the corpus

End-to-end optimization of nonlinear transform codes for perceptual quality (2016, background): “While uniform quantization has been shown to be asymptotically optimal [18], it is well known that dead-zone quantization generally performs better for linear transform coding of images.”
Universal Estimation of Information Measures for Analog Sources (2009, background): “See [29, 30, 60, 61, 91, 92, 102] for generalized results in the approximation of the quantizer output entropy via differential entropy.”
Efficient scalar quantization of exponential and Laplacian random variables (1996, methodology): “optimal ECSQ. This limiting tendency of the optimal ECSQ to approach a UQ also holds for many other distortion measures, as can be shown using the reasoning found in [ 18 ].”
Theoretical foundations of transform coding (2001, methodology): “For entropy-constrained quantization, high resolution analysis shows that it is optimal for each Si to have equal length [9].”
Just noticeable distortion model and its applications in video coding (2005, background): “) source X can be approximated by the following formula when the quantized data are entropy-coded [3,13,12,29]:”
Nonparametric entropy estimation. An overview (1997, background): “Using their own (slightly less general) version of the above statement, Gish and Pierce [25] showed that for the squared distortion D(Q ∆ ), and for the entropy H(Q ∆ ), of the ∆ step-size uniform scalar quantizer, the following asymptotics holds: lim ∆→0 H(Q ∆ ) + 1 2 log(12D(Q ∆ )) = H(f ).”
Joint source channel rate-distortion analysis for adaptive mode selection and rate control in wireless video coding (2002, result): “Our experimental results show that t extended R-D model can accurately estimate the source coding distortion function .”
Towards the Limit of Network Quantization (2016, background): “It is shown in Gish & Pierce (1968) that the uniform quantizer is the optimal high-resolution entropy-constrained scalar quantizer regardless of the source distribution for the mean square error criterion, implying that it is asymptotically optimal in minimizing the mean square quantization error…”
Scalar Quantization for Relative Error (2011, background): “This is related to the number of quantization levels through the approximation R vr ≈ h(x) + log 2 K + E[log 2 λ(x)] [14].”