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We present an approach that takes advantage of multi-packet reception (MPR) to reduce the negative effects of multiple access interference and therefore increase the capacity of an ad hoc network. We analyze the performance upper bound of joint routing and scheduling for ad hoc networks that embrace interference by using MPR. We formulate the optimization problem under a deterministic model and seek to maximize the aggregate network throughput subject to minimum rate requirements. We then propose a polynomial-time heuristic algorithm aimed at approximating the optimal solution to the joint routing and channel access problem under MPR. We show the effectiveness of our heuristic algorithm by comparing its performance with the upper bound.