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In this paper, we consider the Multiple-Access channel with a non uniform energy distribution among users. We point out that, while a space-time code is optimal for the MAC in a balanced scenario, it could become suboptimal in an unbalanced scenario. No CSI is available at the transmitters that are initially assumed to have different energies. We investigate the use of an adapted coding scheme characterized by an unbalanced energy distribution among the symbols that helps compensating the system's unbalance. Numerical results illustrating the outage probability of the channel as well as the error probability of the proposed coding scheme for different power distributions are provided. We show that this unbalanced code is more appropriate in an unbalanced scenario and that it outperforms the best known coding scheme for the MAC.