Towards an Information Theory of Large Networks: An Achievable Rate Region
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We study communication networks of arbitrary size and topology and communicating over a general vector discrete memoryless channel (DMC). We propose an information-theoretic constructive scheme for obtaining an achievable rate region in such networks. Many well-known capacity-defining achievable rate regions can be derived as special cases of the proposed scheme. A few such examples are the physically degraded and reversely degraded relay channels, the Gaussian multiple-access channel, and the Gaussian broadcast channel. The proposed scheme also leads to inner bounds for the multicast and allcast capacities. Applying the proposed scheme to a specific wireless network of n nodes located in a region of unit area, we show that a transport capacity of (n) bit-meters per second (bit-meters/s) is feasible in a certain family of networks, as compared to the best possible transport capacity of (n) bit-meters/s in [16], where the receiver capabilities were limited. Even though the improvement is shown for a specific class of networks, a clear implication is that designing and employing more sophisticated multiuser coding schemes can provide sizable gains in at least some large wireless networks.
