Non-unitary encoding increases the super dense coding capacity in the presence of noise

We study an important protocol in quantum information processing, namely super dense coding in the presence of noise. We compare the optimal super dense coding capacity with unitary and non-unitary encoding. We show that in the case of non-unitary encoding, the optimal capacity can be reached by preprocessing on the sender's side followed by a unitary encoding. We give examples that preprocessing increases the super dense coding capacity.