Analysis of adaptive differential PCM of a stationary Gauss - Markov input
Neil L. Gerr, Stamatis Cambanis · IEEE Transactions on Information Theory · 1987
An adaptive matched differential pulse-code modulator (AMDPCM) is analyzed. The adaptation of the symmetric uniform quantizer parameter\Delta_{n}is performed by fixed multipliers assigned to the quantizer output levels. The input is stationary first-order Gauss-Markov. The correlation of the samples is used as the leakage parameter in the matched integrator, with the predictive reconstruction similarly matched. For a4-level quantizer and multipliers(\gamma^{-1}, \gamma)the limiting joint distribution of the prediction error and\Delta_{n}is derived and the asymptotic sample-point and time-averaged mean-square error (rose) and mean and variance of\Delta_{n}as functions of\gamma \in (1,2]are computed and plotted. It is found that the asymptotic performance of AMDPCM does not depend on the choice of\Delta_{0}, that the increase in mse incurred by using A(M)DPCM instead of (M)DPCM with\Delta_{opt}is small, with mse(A(M)DPCM)\downarrow \min_{\Delta}mse ((M)DPCM) as\gamma \downarrow 1, and that the signal-to-noise ratio of AMDPCM does not depend on the input power.