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MIT/HP Alliance Colloquium: "Multiple-Relay Channel: Coding and Asymptotic Capacity"
Michael Gastpar, Ecole Polytechnique Federale (EPFL), Lausanne, Switzerland, 4-5pm, 36-428.

The multiple-relay channel has stirred interest in the context of wireless ad-hoc networks: how do mobile terminals help each other to boost transmission rates? From a theoretical perspective, the multiple-relay channel is an interesting intermediate step towards understanding more complex networks.

For the single-relay channel, two coding strategies were proposed and analyzed by Cover and El Gamal (IT Sept 1979). The first strategy was extended to multiple relays by Gupta and Kumar (submitted July 2001). The paradigm of this extension is that the source terminal controls the relay terminals; it is thus reminiscent of multiple-antenna transmission. In fact, this strategy achieves capacity when the relays move close to the source.

In this work, we extend the second strategy of Cover and El Gamal. The paradigm of our extension is that the relays compress their channel outputs via Slepian-Wolf coding, and forward the result to the destination. This is related to multiple-antenna reception and, in fact, the strategy achieves capacity when the relays move close to the destination. We argue that our strategy is essential if the full potential of relays is to be exploited.

Good coding schemes for the multiple-relay channel can then be constructed by combining these two fundamental strategies. We illustrate this by the aid of some examples, and again show corresponding asymptotic capacity results.

Finally, we study a simple Gaussian multiple-relay channel and derive its capacity asymptotically as the number of relays tends to infinity. In this case it turns out that uncoded transmission achieves capacity.

This is joint work, in part, with Gerhard Kramer and Piyush Gupta, and, in part, with Martin Vetterli.

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