The resulting frequency-domain data is broken into noise floor and residue components, and then quantized and entropy coded using a codebook-based vector quantization algorithm.
Since these lossless data compression steps don't add noise into, or otherwise change the contents (unlike quantization), it is sometimes referred to as noiseless coding.
Essentially, when any sample's bit depth is reduced, the quantization error between the rounded (truncated) value and the original value is measured and stored.
Color quantization helped to justify this tradeoff by making it possible to display many high color images in 16- and 256-color modes with limited visual degradation.