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

An adaptive matched differential pulse-code modulator (AMDPCM) is analyzed. The adaptation of the symmetric uniform quantizer parameterΔₙis 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(γ⁻¹, γ)the limiting joint distribution of the prediction error andΔₙis derived and the asymptotic sample-point and time-averaged mean-square error (rose) and mean and variance ofΔₙas functions ofγ ∈ (1,2]are computed and plotted. It is found that the asymptotic performance of AMDPCM does not depend on the choice ofΔ₀, that the increase in mse incurred by using A(M)DPCM instead of (M)DPCM withΔₒₚₜis small, with mse(A(M)DPCM)↓ minΔmse ((M)DPCM) asγ ↓ 1, and that the signal-to-noise ratio of AMDPCM does not depend on the input power.