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Gaussian Approximation of Quantization Error for Estimation From Compressed Data

https://doi.org/10.1109/TIT.2021.3083271

Kipnis, Alon; Reeves, Galen (August 2021, IEEE Transactions on Information Theory)

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Gaussian Approximation of Quantization Error for Estimation from Compressed Data

https://doi.org/10.1109/ISIT.2019.8849826

Kipnis, Alon; Reeves, Galen (July 2019, 2019 IEEE International Symposium on Information Theory (ISIT))

We consider the statistical connection between the quantized representation of a high dimensional signal X using a random spherical code and the observation of X under an additive white Gaussian noise (AWGN). We show that given X, the conditional Wasserstein distance between its bitrate-R quantized version and its observation under AWGN of signal-to-noise ratio 2^{2R - 1} is sub-linear in the problem dimension. We then utilize this fact to connect the mean squared error (MSE) attained by an estimator based on an AWGN-corrupted version of X to the MSE attained by the same estimator when fed with its bitrate-R quantized version.
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Single Letter Formulas for Quantized Compressed Sensing with Gaussian Codebooks

https://doi.org/10.1109/ISIT.2018.8437761

Kipnis, Alon; Reeves, Galen; Eldar, Yonina C. (June 2018, 2018 IEEE International Symposium on Information Theory (ISIT))

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