The orthogonal coding scheme, known to asymptotically achieve the
capacity per unit cost (CPUC) for single-user ergodic memoryless
channels with a zero-cost input symbol, is investigated for single-user
compound channels, which exhibit uncertainties in their input-output
relationships. A minimax formulation is adopted to attain robustness.
First, a class of achievable rates per unit cost (ARPUC) is derived, and
its utility is demonstrated through several representative case studies.
Second, when the channel uncertainty satisfies a convexity property,
optimization is performed over the class of ARPUC to yield a lower bound
to the CPUC, through utilizing results of minimax robustness. This CPUC
lower bound indicates the ultimate performance of the orthogonal coding
scheme, and coincides with the CPUC under certain restrictive
conditions. Finally, still under the convexity property, it is shown
that the CPUC can generally be achieved, through utilizing so-called
mixed strategies in which orthogonal codes with different nonzero-cost
input symbols are time-shared with appropriately chosen frequencies.