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We present the idea of process assignment as a basic tool to provide operational compression bounds. We give a simple proof for the operational rate distortion function using process assignment arguments for ergodic and stationary systems. We generalize the problem to multiterminal systems. A terse review of random process theory is followed by two examples in communications and computers industry, where this theory supplies key bounds to the network performance. ; Coupling the process definitions with the mathematical stochastic representation of process assignment provides a new and simple proof of the achievable rate region for a degraded diversity system, or a multiple-description system. The proof can be extended to more complicated communications networks. The equivalence of Shannon-type and operational bounds is also addressed.