  The channel reliability function is an important tool that characterizes the
reliable transmission of messages over communication channels. For many
channels, only upper and lower bounds of the function are known. We analyze the
computability of the reliability function and its related functions. We show
that the reliability function is not a Turing computable performance function.
The same also applies to the functions related to the sphere packing bound and
the expurgation bound. Furthermore, we consider the $R_\infty$ function and the
zero-error feedback capacity, since they play an important role in the context
of the reliability function. Both the $R_\infty$ function and the zero-error
feedback capacity are not Banach Mazur computable.
