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