Exploiting the finite-alphabet property for cooperative relays

We consider, in this paper, the design of a cooperative relay strategy by exploiting the finite-alphabet property of the source. Assuming a single source-sink pair with L relay nodes all communicating in orthogonal channels, we derive necessary conditions for optimal relay signaling that minimizes the error probability at the sink node. The derived conditions allow us to construct an iterative algorithm to find the distributed relay signaling that is at least locally optimal. As a byproduct, one can show that the so-called decode-and-forward (DF) relay scheme does not satisfy the necessary condition hence is not optimal in its error probability performance. Indeed, numerical examples show that the proposed scheme provides substantial performance improvement over both DF and the amplify-and-forward approach.