Dither & Noise Shaping
The introduction to quantization and quantization error showed that the quantization error is correlated with the input signal. Athough this can be desirable for a distortion-like audio effect, it can be a problem in analog-digital conversion and bit-depth conversion.
Dither can be used to decorrelate the signal and the noise - it is additional noise that is added to the input signal before the quantization.
Quantization ErrorΒΆ
$$ e = x-x* $$
PMFΒΆ
SpectrumΒΆ
Noise ShapingΒΆ
While the applied dither does change the qualities of the quantization, it does not necessarily improve them a lot for the 3-Bit case. The noise - though now uncorrelated, is very dominant with this low SNR.