Bounding of MAP decode and forward relaying

We formulate the maximum a posteriori (MAP) rule for the decode-and-forward transmission strategy operating with a noisy relay. From the MAP rule we derive an analytical bound on the error probability, taking into account decoding errors at the relay. We further determine a practical close-to-MAP decoding scheme based on a convenient error model for the decoding operation at the relay. This error model allows for a trellis representation of the code described jointly by the encoding process at the source and the re-encoding process at the relay. Numerical results demonstrate a close agreement between our analytical results and monte carlo simulations.