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Information Capacity with Input Cost

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Definition
InfoTheory

The information capacity (or information capacity-cost function) of a discrete-time continuous memoryless channel (X,Y,fYX)(\mathcal{X},\mathcal{Y},f_{Y|X}) with input average cost constraint (t(),P)(t(\cdot),P) is given by C(P):=supFX:E[t(X)]PI(X;Y)(in bits)\tag{in bits}C(P):=\sup_{F_{X}:E[t(X)]\le P}I(X;Y)where the supremum is taken over all input distributions FXF_{X} and I(X;Y)I(X;Y) is the channel’s input-output mutual information.

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