Code Excited Linear Prediction (CELP) coders are state-of-the-art in telephony coding:
The theory says that after all the linear correlations have been removed, the prediction residual is uncorrelated values with a Gaussian distribution. Therefore generate the excitation codebook as a set of random numbers.
Complete system looks like figure 48:
Figure 48: Typical CELP coder
Where all parameters of the system are obtained by minimising the final mean squared error. Sequential parameter estimation is non-optimal.