Analysis of adaptive differential PCM of a stationary Gauss - Markov input

Abstract

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 a 4 -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.