On the capacity of asymptotically memoryless continuous-time channels (Corresp.)

Previously, a coding theorem and its converse for stationary asymptotically memoryless continuous-time channels were proved, giving the capacity
C
with an almost sure constraint on the input cost. For calculation, it is more convenient to find a capacity
\bar{C}
with the constraint on the expected input cost. Obviously,
C \leq \bar{C}
, but the coding theorem may not hold for
\bar{C}
. For a class of input costs typified by the time-average power, we prove the coding theorem for
\bar{C}
by directly showing
C = \bar{C}
.