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Information content in Gaussian noise: optimal compression rates

August Romeo·Enrique Gaztanaga·Jose Barriga·Emilio Elizalde
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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.), $f^{n_p}$ power-law noise ---including $1/f$ noise---, (w.n.$+1/f$) noise, and piecewise (w.n.+$1/f |$ w.n.$+1/f^2$) noise are discussed, while quantitative behaviours and useful approximations are provided.

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August Romeo, Enrique Gaztanaga, Jose Barriga, Emilio Elizalde. 1999-11-11. Information content in Gaussian noise: optimal compression rates. https://doi.org/10.1142/s0129183199000528

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