  We investigate the use of noisy entanglement as a resource in classical
communication via a quantum channel. In particular, we are interested in the
question whether for any entangled state, including bound entangled states,
there exists a quantum channel the classical capacity of which can be increased
by providing the state as an additional resource. We partially answer this
question by showing, for any entangled state, the existence of a quantum memory
channel the feedback-assisted classical capacity with product encodings of
which can be increased by using the state as a resource. Using a different
(memoryless) channel construction, we also provide a sufficient entropic
condition for an advantage in classical communication (without feedback and for
general encodings) and thus provide an example of a state that is not
distillable by means of one-way local operations and classical communication
(LOCC), but can provide an advantage in the classical capacity of a number of
quantum channels. As separable states cannot provide an advantage in classical
communication, our condition also provides an entropic entanglement witness.
