Capacity Region for Multiple-Access Channels Employing Relay Nodes

Almost all problems in multi-terminal information theory stem from Slepian-Wolf coding problem and a coding problem for multiple access channels (MACs). Cover et al. considered a joint source-channel coding problem and integrated these two problems. One typical example of the communication model proposed by Cover et al. is a sensor network. However, in usual sensor networks, the transmission power of sensors is so small that each sensor cannot send the message to the data center directly, but the nearest relay or edge node, and the relay node resends the message to the data center through a backborn network. We model such a sensor network as MACs employing relay nodes that consist of a cascade of point-to-point channels and a MAC. We show a sufficient condition and a necessary condition for reliable communication over a MAC employing relay nodes. Moreover, we show that both conditions coincide if the sources are independent.