  We present a formal quantum mechanical analysis of the communication protocol
of Prevedel {\it et al.}\ [Phys. Rev. Lett. \textbf{106}, 110505 (2011)], in
which entanglement shared by sender and receiver is used to enhance, beyond
that achievable via the optimal classical strategy, the probability of
successful transmission of a bit through a particular noisy classical channel
${\cal N}$. We provide a full analysis of this protocol when the shared
entanglement resides in a two-qubit system. Our analysis shows the measurement
choices specified by the protocol yield the maximum possible enhancement of the
probability of successful communication of the bit with one use of the channel
${\cal N}$. We determine that shared entanglement residing in a two-qudit
system with $d > 2$ cannot provide enhancement beyond that produced by
entangled qubits. Finally, we show how the protocol should be extended when
probability parameters for the channel ${\cal N}$ are allowed to vary.
