On fidelity per unit cost

We consider source coding with a fidelity criterion, channel coding with a channel input constraint, and the combined problem of reproducing a source across a noisy channel. All three cases face a similar tradeoff between resource and performance, and the operating point with the highest performance per resource is of particular interest. In the case of channel coding, channel input cost is traded for rate, and the optimal tradeoff corresponds to the capacity per unit cost. We define equivalent notions for the other two cases and show how they relate. For each case we give necessary and sufficient conditions for the optimal tradeoff to be achieved.