Information content in Gaussian noise: optimal compression rates

We approach the theoretical problem of compressing a signal dominated by gaussian noise. We present accurate 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 of the noise P (f). Further, we show how the entropy and the compression rate depend on the shape of this power spectrum, given different normalizations. The cases of white noise (w.n.), power-law noise fp –including 1/f noise–, (w.n. + 1/f) noise, and piecewise (w.n. + 1/f + 1/f) noise are discussed in detail, while quantitative behaviours and useful approximations are provided.