An analytical expression of the probability of error for relaying with decode-and-forward

For a three-node relay network that employs binary linear codes and the decode-and-forward strategy, we derive analytic upper and lower bounds for the probability of error at the destination. The bounds are based on union-bound techniques and the input-output weight enumerator of the encoder. As an application, we use this bound to optimise the decoder at the destination. Our approach is verified by simulation results.