1 N ov 1 99 9 Information content in uniformly discretized Gaussian noise : optimal compres - sion rates

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.), fp power-law noise —including 1/f noise—, (w.n.+1/f) noise, and piecewise (w.n.+1/f | w.n.+1/f) noise are discussed, while quantitative behaviours and useful approximations are provided.