  In this correspondence, we illustrate among other things the use of the
stationarity property of the set of capacity-achieving inputs in capacity
calculations. In particular, as a case study, we consider a bit-patterned media
recording channel model and formulate new lower and upper bounds on its
capacity that yield improvements over existing results. Inspired by the
observation that the new bounds are tight at low noise levels, we also
characterize the capacity of this model as a series expansion in the low-noise
regime.
  The key to these results is the realization of stationarity in the
supremizing input set in the capacity formula. While the property is prevalent
in capacity formulations in the ergodic-theoretic literature, we show that this
realization is possible in the Shannon-theoretic framework where a channel is
defined as a sequence of finite-dimensional conditional probabilities, by
defining a new class of consistent stationary and ergodic channels.
