  The rate regions of many variations of the standard and wire-tap channels
have been thoroughly explored. Secrecy capacity characterizes the loss of rate
required to ensure that the adversary gains no information about the
transmissions. Authentication does not have a standard metric, despite being an
important counterpart to secrecy. While some results have taken an
information-theoretic approach to the problem of authentication coding, the
full rate region and accompanying trade-offs have yet to be characterized. In
this paper, we provide an inner bound of achievable rates with an average
authentication and reliability constraint. The bound is established by
combining and analyzing two existing authentication schemes for both noisy and
noiseless channels. We find that our coding scheme improves upon existing
schemes.
