Process definitions of distortion-rate functions and source coding theorems

The standard definition of the distortion-rate function involves a limit of information-tbeoretic minimizations over distributions of random vectors. Several alternative definitions, each involving a single minimization over random processes, are presented here and verified. These definitions parallel Khinchine´s process definition of channel capacity, provide a new interpretation of block and nonblock source coding (with a fidelity criterion) theorems in terms of optimal stochastic codes, and provide a comparison between the optimal performance theoretically attainable (OPTA) using block and nonblock source codes. Coupling the process definitions with recently developed bounding techniques provides a new and simple proof of the block source coding theorem for ergodic sources.