Convergence of the projection method for an autoregressive process and a matched DPCM code

The key step in the analysis of differential pulse code modulation (DPCM) is to find the steady-state probability distribution of a random process in terms of which the code distortion can be evaluated. For the case of an autoregressive source and a matched DPCM code, a well-known approximation technique has been used for the evaluation of the steady-state distribution of the prediction error process. However, the validity of this approximation method has not been justified before. A framework in which this approximation technique can be viewed as the projection method for the solution of integral equations is established. Sufficient conditions under which the approximation method can be rigorously justified are obtained.>