On the capacity of burst noise-erasure channels with and without feedback

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 satisfy a so-called “quasi-symmetry” condition 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 nonfeedback 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.