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We consider multi-hop multiple access (MAC) and broadcast channels (BC) where communication takes place with the assistance of relays that amplify and forward (AF) their received signals. For a two hop parallel AF relay MAC, assuming a sum power constraint across all relays we characterize optimal relay amplification factors and the resulting capacity regions. We find that the parallel AF relay MAC with total transmit power of the two users È ½ · È ¾ È and total relay power È Ê is the dual ofdoi:10.1109/pimrc.2007.4394547 dblp:conf/pimrc/JafarGH07 fatcat:dnkuvsy2nbb5lpdyvksbrlds2m