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In this paper, the problem of power allocation and optimal decoding order of users for the uplink channel of a multirate direct-sequence code-division multiple-access system with linear successive interference cancellation (IC) is addressed. First, the closed-form expressions of the required received powers at the base station for providing all users with their demanded rates and signal to interference-plus-noise ratios (SINRs) are derived. Then, it is shown that, unlike the case when the IC is perfect, in this case, optimum ordering of users at the receiver, which minimizes the total transmitted power, is a function of both their requested SINRs and path gains. Finally, in searching for the optimal ordering of users, an upper bound is found for the ratio between the path gain of the user with a higher requested SINR to the path gain of the user with a lower demanded SINR, which should be greater than the value which would assure that decoding the user with a higher SINR prior to the other one would be energy-conserving.