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Leveraging recent progress in compute-and-forward the authors propose an approach to random access that is based on physical-layer network coding: When packets collide, it is possible to recover a linear combination of the packets at the receiver. Over many rounds of transmission, the receiver can thus obtain many linear combinations and eventually recover all original packets. This is by contrast to slotted ALOHA where packet collisions lead to complete erasures. The throughput of the proposed strategy is derived for a system with two users and shown to be significantly superior to the best known strategies, including multi-packet reception.
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