Differential pulse-code modulation of the Wiener process

The performance of DPCM (Differential Pulse Code Modulation) with uniform quantization with the Wiener process input is analyzed. The approach taken is to establish an equation for the characteristic function of error distribution and then to solve its steady-state version. No use is made in the derivation of the approximating concepts of slope overload error and granular error. Exact formulas are derived which give the mean-squared-error in terms of the step size 2Δ and the number of levels
N
of quantization. Curves are shown for two kinds of mean-squared-error versus Δ or
N
, and are compared with the rate distortion function.