Quantization error and step-size distributions in ADPCM

An adaptive differential pulse code modulator (ADPCM) with a finite number of possible step-sizes and a leaky integrator in the feedback loop is considered. A zero-mean unit-ariance first-order Markov sequence is chosen as the input to thc system, and the leak parameter of the ADPCM accumulator is made equal to the intersample correlation of the input sequence. Using this fundamental structure, a method is presented for computing the exact joint probability distribution function of quantization error and step-size in ADPCM. From the joint distribution, marginal quantization error, and step-size distributions are obtained for Gauss-Markov, exponential-Markov, and uniform-Markov input signals. Empirical distributions obtained from simulations agree very well with their theoretical counterparts.