Technical Program

Paper Detail

Paper Title Gaussian Approximation of Quantization Error for Estimation from Compressed Data
Paper IdentifierTH2.R6.1
Authors Alon Kipnis, Stanford University, United States; Galen Reeves, Duke University, United States
Session Lossy Compression
Location Sorbonne, Level 5
Session Time Thursday, 11 July, 11:40 - 13:00
Presentation Time Thursday, 11 July, 11:40 - 12:00
Manuscript  Click here to download the manuscript
Abstract 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.