  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.
