Differential encoder design using stochastic control theory

The design of a differential encoder for data compression is formulated as a stochastic optimal control problem. The resulting plant to be controlled contains control-dependent noise, but the observation model is noise-free. It is shown that the optimal one-stage control is the prediction error, and therefore, the classical differential pulse code modulation system is optimal for this criterion. The optimal multistage control is shown to include a scaled version of the one-stage control and a weighted sum of the differences between the past inputs and their estimates. Simulation results are presented for a first order differential pulse code modulation system. Four, eight, and twelve level adaptive quantizers are used in the simulations.