The Amplify-based Multiple-Relay Multiple-Access Channel: Capacity Region and MAC-BC Duality

We consider the multiple access channel (MAC) assisted by N parallel relays that only have buffering and amplifying capabilities. For this channel, we derive the capacity region applying results on MAC with finite memory. Later, the MAC-broadcast (BC) duality is demonstrated using duality arguments for vector channels. Indeed, the capacity region of the Gaussian amplify-based BC with N parallel relays is shown to be the capacity region of the amplify-based MAC with sum power constraint, and to be achievable through dirty paper coding.