On the capacity of wireless networks: the relay case

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Abstract
In (1), Gupta and Kumar determined the capac- ity of wireless networks under certain assumptions, among them point-to-point coding, which excludes for example multi-access and broadcast codes. In this paper, we consider essentially the same physical model of a wireless network under a different traffic pattern, namely the relay traffic pattern, but we allow for arbitrar- ily complex network coding. In our model, there is only one active source/destination pair, while all other nodes assist this transmis- sion. We show code constructions leading to achievable rates and derive upper bounds from the max-flo w min-cut theorem. It is shown that lower and upper bounds meet asymptotically as the number of nodes in the network goes to infinity , thus proving that the capacity of the wireless network with nodes under the re- lay traffic pattern behaves like bits per second. This demon- strates also that network coding is essential: under the point-to- point coding assumption considered in (1), the achievable rate is constant, independent of the number of nodes. Moreover, the result of this paper has implications and exten- sions to fading channels and to sensor networks.

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