  We study multipartite super dense coding in the presence of a covariant noisy
channel. We investigate the case of many senders and one receiver, considering
both unitary and non-unitary encoding. We study the scenarios where the senders
apply local encoding or global encoding. We show that, up to some
pre-processing on the original state, the senders cannot do better encoding
than local, unitary encoding. We then introduce general Pauli channels as a
significant example of covariant maps. Considering Pauli channels, we provide
examples for which the super dense coding capacity is explicitly determined.
