Relay computation: Managing interference with structure and cooperation

We examine the benefits of relay cooperation to compute-and-forward. We study a system with two sources, two destinations, and a dedicated relay, in which the destinations decode finite-field linear combinations of sources´ messages. We present inner and outer bounds on the computation rate region under two relay modalities: the standard relay and the instantaneous relay, or “relay-without-delay.” For the standard relay, we develop a compress-and-forward scheme based on block Markov encoding. This scheme improves the achievable computation rate, but it appears not to increase the achieved degrees-of freedom. For the instantaneous relay, we develop a memoryless amplify-and-forward scheme which, in addition to improving the achievable computation rate, increases the achieved DoFs to the maximum of two. In this case, relay cooperation provides degrees-of-freedom optimality while retaining good performance at finite signal-to-noise ratios.