Title :
On the statistics of the error in predictive coding for stationary Ornstein-Uhlenbeck processes
Author :
Koski, Timo ; Cambanis, Stamatis
Author_Institution :
Dept. of Syst. Eng. & Math., Lulea Univ. of Technol., Sweden
fDate :
5/1/1992 12:00:00 AM
Abstract :
Explicit expression are derived for the conditional expectation and variance of the encoder in a predictive DPCM coder with an N-level quantizer, when a stationary Ornstein-Uhlenbeck process is a source. A representation of the encoder in terms of a stochastic integral is presented. These expressions yield a nonlinear stochastic difference equation for the decoding error process and a stochastic differential equation (SDE) as a weak limit for the error process. The statistical properties of the error obtained as a solution of the limiting SDE are interpreted in terms of the slope overload error
Keywords :
decoding; difference equations; differential equations; encoding; error statistics; filtering and prediction theory; pulse-code modulation; stochastic processes; DPCM coder; N-level quantizer; conditional expectation; decoding error process; encoder; error statistics; nonlinear stochastic difference equation; predictive coding; slope overload error; stationary Ornstein-Uhlenbeck processes; stochastic differential equation; stochastic integral; variance; Decoding; Delta modulation; Difference equations; Differential equations; Error analysis; Nonlinear equations; Predictive coding; Pulse modulation; Stability; Stochastic processes;
Journal_Title :
Information Theory, IEEE Transactions on
