Information content in Gaussian noise: optimal compression rates
August Romeo, Enrique Gaztanaga, Jose Barriga, Emilio Elizalde
Abstract
We approach the theoretical problem of compressing a signal dominated by Gaussian noise. We present expressions for the compression ratio which can be reached, under the light of Shannon's noiseless coding theorem, for a linearly quantized stochastic Gaussian signal (noise). The compression ratio decreases logarithmically with the amplitude of the frequency spectrum P(f) of the noise. Entropy values and compression rates are shown to depend on the shape of this power spectrum, given different normalizations. The cases of white noise (w.n.), fnp power-law noise ---including 1/f noise---, (w.n.+1/f) noise, and piecewise (w.n.+1/f | w.n.+1/f2) noise are discussed, while quantitative behaviours and useful approximations are provided.
Create a lesson
Related papers
Reduced latent leakage does not reliably predict lower likelihood bias in collider inference
Tong Pan
The Greedy Bump Bias: Local Profiling Geometry and the Look-Elsewhere Effect
Tommaso Dorigo
Multi-fidelity Monte Carlo estimation of floor response spectra under combined seismic and structural parameter uncertainties
Nils Baillie, Baptiste Kerleguer, Cyril Feau et al.
Parameter inference from a non-stationary unknown process using statistical feature-based slow feature analysis
Kieran S. Owens, Masako Tamaki, Ben D. Fulcher
A Probability Model for Pentagonal Prism Dice Rolls
Paul R. Hurst, J. Naleo Hyde
Geometry-native machine learning reconstruction of DSMC moment fields with support monitoring
Ehsan Roohi