Epsilon-Capacity of a Class of Nonergodic Channels

We consider the nonergodic channel model obtained by averaging binary symmetric channel components with respect to a weighting distribution. For a fixed epsi isin (0,1), suppose one wishes to compute the e-capacity of the nonergodic channel model, which is the optimum asymptotic rate at which the channel can be encoded via a sequence of channel codes which each yield maximal probability of decoding error les epsi. In 1963, Parthasarathy provided a formula for epsi-capacity valid for all but at most countably many values of epsi. Parthasarathy's formula fails at precisely those epsi values in (0,1) at which the epsi-capacity function undergoes a discontinuity. We present a formula for the epsi-capacity function which is valid at a discontinuity whenever the jump in the epsi-capacity function at that discontinuity is not too large