  A class of burst noise-erasure channels which incorporate both errors and
erasures during transmission is studied. The channel, whose output is
explicitly expressed in terms of its input and a stationary ergodic
noise-erasure process, is shown to have a so-called "quasi-symmetry" property
under certain invertibility conditions. As a result, it is proved that a
uniformly distributed input process maximizes the channel's block mutual
information, resulting in a closed-form formula for its non-feedback capacity
in terms of the noise-erasure entropy rate and the entropy rate of an auxiliary
erasure process. The feedback channel capacity is also characterized, showing
that feedback does not increase capacity and generalizing prior related
results. The capacity-cost function of the channel with and without feedback is
also investigated. A sequence of finite-letter upper bounds for the
capacity-cost function without feedback is derived. Finite-letter lower bonds
for the capacity-cost function with feedback are obtained using a specific
encoding rule. Based on these bounds, it is demonstrated both numerically and
analytically that feedback can increase the capacity-cost function for a class
of channels with Markov noise-erasure processes.
