Upper-Bounding the Capacity of Relay Communications - Part II
  This paper focuses on the capacity of peer-to-peer relay communications wherein the transmitter are assisted by an arbitrary number of parallel relays, i.e. there is no link and cooperation between the relays themselves. We detail the mathematical model of different relaying strategies including cutset and amplify and forward strategies. The cutset upper bound capacity is presented as a reference to compare another realistic strategy. We present its outer region capacity which is lower than that in the existing literature. We show that a multiple parallel relayed network achieves its maximum capacity by virtue of only one relay or by virtue of all relays together. Adding a relay may even decrease the overall capacity or may do not change it. We exemplify various outer region capacities of the addressed strategies with two different case studies. The results exhibit that in low signal-to-noise ratio (SNR) environments the cutset outperforms the amplify and forward strategy and this is contrary in high SNR environments. 
Farshad Shams, Marco Luise
cs.IT math.IT