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

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2 Author(s)

An adaptive matched differential pulse-code modulator (AMDPCM) is analyzed. The adaptation of the symmetric uniform quantizer parameterDelta_{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 andDelta_{n}is derived and the asymptotic sample-point and time-averaged mean-square error (rose) and mean and variance ofDelta_{n}as functions ofgamma in (1,2]are computed and plotted. It is found that the asymptotic performance of AMDPCM does not depend on the choice ofDelta_{0}, that the increase in mse incurred by using A(M)DPCM instead of (M)DPCM withDelta_{opt}is small, with mse(A(M)DPCM)downarrow min_{Delta}mse ((M)DPCM) asgamma downarrow 1, and that the signal-to-noise ratio of AMDPCM does not depend on the input power.

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Information Theory, IEEE Transactions on  (Volume:33 ,  Issue: 3 )