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 $1\to 0$ and $0 \to 1$ can be large. Practically, one can assume that only one type of error can occur. These errors arecalled asymmetric. Unidirectional errors differ from asymmetric type of errors; here both $1 \to 0$ and $0 \to 1$ type of errors are possible, but in any submittedcodeword 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 the capacity error function. It turns out that the bounds depend on the parity of the alphabet $q$. 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.