\begin{abstract}
This paper introduces the notions of
variable-to-fixed and fixed-to-variable channel capacity.
For channels that satisfy the strong converse, these
notions coincide with the conventional Shannon capacity.
For channels that do not behave ergodically,
the conventional fixed-rate Shannon capacity 
only depends on least-favorable channel conditions,
while the variable-rate capacity notions are
able to capture the whole range of channel states
and their likelihood, even in the absence 
of any side information
about channel state at the transmitter.
We show that (single-user)
variable-rate channel capacity
is intimately connected to the
capacity region of broadcast channels with degraded message sets.
 \end{abstract}