Robust message recovery for non-cooperative compute-and-forward relaying

Compute-and-Forward relaying schemes exploit the additive nature of the wireless channel for decoding linear equations/combinations of transmitted messages. However, decoding equations that maximize the computation rate at each relay is in general not optimal from the network perspective. In fact, the (destination) receiver may fail to recover the individual messages even when the relays have successfully decoded linear combinations of them. This paper introduces an easy to implement non-cooperative practical scheme using short linear codes that guarantees a message recovery at the receiver given a successful recovery of linear combinations. We achieve this by putting additional constraints at the relays, which allows us to convert the shortest vector problem into a closest vector problem solvable in polynomial complexity.