  We investigate the distributed dense coding (DC) protocol, involving multiple
senders and a single or two receivers under the influence of non-Markovian
noise, acting on the encoded qubits transmitted from senders to the
receiver(s). We compare the effects of non-Markovianity on DC both for the
dephasing and depolarising channels. In the case of dephasing channels, we
illustrate that for some classes of states, high non-Markovian strength can
eradicate the negative influence of noisy channels which is not observed for
depolarizing noise. Furthermore, we incorporate randomness into the noise
models by replacing the Pauli matrices with random unitaries and demonstrate
the constructive impact of stochastic noise models on the quenched averaged
dense coding capacity. Interestingly, we report that the detrimental effect of
non-Markovian depolarising channels in the DC protocol can be eliminated when
randomness is added to the channel.
