Definition

For a closed-loop predictive quantizer we define the system SNR in terms of the closed-loop prediction gain, $G_{\text{clp}}$ and coding gain $G_{Q}$ (not in dB) $$\text{SNR}_{\text{sys}}=G_{\text{clp}}G_{Q}=\frac{E[X_{n}^{2}]}{E[e_{n}^{2}]}\frac{E[e_{n}^{2}]}{E[(e_{n}-\hat{e}_{n})^{2}]}$$or simply in dB as: $$\text{SNR}_{\text{sys}}=10\log_{10}G_{\text{clp}}+\text{SNR}_{Q} \ \ \ [\text{dB}]$$ ## Note $G_{\text{clp}}$ and $G_{Q}$ are interdependent hence we cannot fix one to maximize the other.

Increasing $G_{\text{clp}}$ does not necessarily increase $\text{SNR}_{\text{sys}}$, although in practice it usually does.