  We consider the fundamental protocol of dense coding of classical information
assuming that noise affects both the forward and backward communication lines
between Alice and Bob. Assuming that this noise is described by the same
quantum channel, we define its dense coding capacity by optimizing over all
adaptive strategies that Alice can implement, while Bob encodes the information
by means of Pauli operators. Exploiting techniques of channel simulation and
protocol stretching, we are able to establish the dense coding capacity of
Pauli channels in arbitrary finite dimension, with simple formulas for
depolarizing and dephasing qubit channels.
