  Entanglement and entanglement-assisted are useful resources to enhance the
mutual information of the Pauli channels, when the noise on consecutive uses of
the channel has some partial correlations. In this paper, We study quantum
communication channels with correlated noise and derive a general expression
for the mutual information of quantum channel, for the product, maximally
entangled state coding and entanglement-assisted systems with correlated noise
in the Pauli quantum channels. Hence, we suggest more efficient coding in the
entanglement-assisted systems for the transmission of classical information and
derive a general expression for the entanglement-assisted classical capacity.
Our results show that in the presence of memory, a higher amount of classical
information is transmitted by two or four consecutive uses of
entanglement-assisted systems.
