Asymptotically Optimal Scheduling for Compute-and-Forward
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Consider a Compute and Forward (CF) relay network with L users and a single relay. The relay tries to decode a linear function of the transmitted signals. For such a network, letting all L users transmit simultaneously, especially when L, is large causes a significant degradation in the rate the relay is able to decode. In fact, it goes to zero very fast with L. Therefore, in each transmission phase only a fixed number of users should transmit, i.e., users should be scheduled. In this work, we provide an asymptotically optimal, polynomial time scheduling algorithm for CF. We show that scheduling under CF not only guarantees non-zero rate, it provides a gain in the system sum-rate, up to the optimal scaling law of O(L). We do this by first fixing a good, yet sub-optimal, coefficients vector, and devising a polynomial time algorithm to find a sub-set of the users whose channel gains matches the vector. We then prove that this choice is asymptotically optimal.
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