Decoding scheme for relay networks with parity forwarding cooperation protocol

The maximum a posterior (MAP) decoding scheme is presented here for cooperative communication networks that adopt the parity forwarding as a cooperation protocol. The MAP decoder is optimal in the sense that it minimises the error probability. The authors consider a wireless network that is composed of two sources: two relays and a single destination. A closed-form expression is derived for upper bound on the bit error probability. The complexity of derivation comes from the fact that although the source generates data with equal probability, the data received at the destination does not have the same a priori probability. That is because of the error that occurs in the source-to-relay link. Therefore, the MAP decoding rule cannot be simplified to the maximum likelihood decoding rule. The results show that the analytical upper bound is very tight and almost coincides with the exact error probability obtained from simulations at higher values of the signal-to-noise ratio. Accordingly, the closed-form expression of the upper bound can be used to fully study and understand the diversity performance of the system.