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

Abstract

In digital systems such as fiber optical communications, the ratio between probability 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 where the errors have magnitude one and give bounds for the capacity error function. It turns out that the bounds depend on the parity of the alphabet size q. Furthermore, we show that for feedback, the capacity error function for the binary asymmetric channel is different from the symmetric channel. This is in contrast to the behavior of the function without feedback.