On fidelity per unit cost

Abstract

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.

Computation of Channel Capacity Based on Self‐Concordant Functions

“…It seems that we should add q j > 0 as constraints for (22) since there are log q j in the objective function of (22). But the q j are not independent variables.…”

“…The objective function of (27) is self-concordant, so we can solve (27) by the path-following method. Channel capacity per unit cost is one of the typical problems of channel capacity with constraints [15,[20][21][22]. By [15], channel capacity per unit cost can be computed by…”