  In "Reliable Communication in the Absence of a Common Clock" (Yeung et al.,
2009), the authors introduce general run-length sets, which form a class of
constrained systems that permit run-lengths from a countably infinite set. For
a particular definition of probabilistic capacity, they show that probabilistic
capacity is equal to combinatorial capacity. In the present work, it is shown
that the same result also holds for Shannon's original definition of
probabilistic capacity. The derivation presented here is based on generating
functions of constrained systems as developed in "On the Capacity of
Constrained Systems" (Boecherer et al., 2010) and provides a unified
information-theoretic treatment of general run-length sets.
