Definition (Scalar Quantizer)

An $N$-point scalar quantizer is a mapping $$Q:\mathbb{R}\to \mathcal{C}$$where $\mathcal{C}=\{ y_{1},\dots,y_{N} \}\subset \mathbb{R}$ is the codebook and each $y_{i}, \ i=1,\dots,N$ is called a reproduction point.