We investigate the use of non-binary classical error-correcting codes in facilitating reliable, entanglement-assisted communication of classical information over quantum depolarising channels. A classical-quantum communication system is presented, which relies on error-correction in the classical domain to achieve an information rate that approaches the entanglement-assisted capacity of the quantum channel. Classical information is transmitted over the channel by means of the superdense coding protocol, and the impact of the noisy distribution of initial entanglement resources on the achievable information rate is considered. In this context, the transmission model is equivalent to a non-binary discrete symmetric classical channel, which motivates the use of non-binary error-correcting codes capable of exploiting correlations between the pairs of classical bits communicated via the superdense coding protocol. We illustrate this principle by showing that duo-binary turbo codes significantly outperform binary turbo codes in the considered scenarios.