Bounds for the capacity error function for unidirectional channels with noiseless feedback

In digital systems such as fiber optical communications, the ratio between probability the of errors of type 1 → 0 and 0 → 1 can be large. Practically, one can assume that only one type of error can occur. These errors are called asymmetric. Unidirectional errors differ from asymmetric type of errors; here both 1 → 0 and 0 → 1 type of errors are possible, but in any submitted codeword all the errors are of the same type. This can be generalized for the q-ary case. We consider q-ary unidirectional channels with feedback and give bounds for their capacity error functions. It turns out that the bounds depend on the parity of the alphabet q. Furthermore, we show that for the feedback case, the capacity error functions of the binary asymmetric channel and the symmetric channel are not the same. This is in contrast to the behavior of those functions without feedback.