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This paper tackles a power minimization problem of interleave-division multiple-access (IDMA) systems over a fading multiple-access channel. The problem is minimizing the total power received by the receiver while keeping the bit error rates (BERs) of all users below a predefined value. The original formulation of the problem has highly nonlinear and implicitly defined functions, which render most existing optimization methods incapable. A new formulation is proposed in this paper, whose solution can effectively be obtained by a branch-and-bound (B&B) technique. An algorithm is devised based on B&B, and its effectiveness is also demonstrated by numerical experiments of systems with a moderate numbers of users.