“The first phase [of life] you believe in Santa Claus, the second you don’t believe in Santa Clause, and in the third you become Santa Claus.” — Tony Ephremides
Prof. Anthony Ephremides gave the third plenary at ISIT, which included an interim report on the consummation between information theory and network coding and many connections between opera and research. He did a great job I think in explaining the difference between throughput region, stability region, and capacity region (under bursty vs. non-bursty use). These are in increasing order of inclusion. Some interesting tidbits (some new, some not):
- He had a complaint about the way networking handles fading by simply saying the success probability for a packet being received is just .
- Under contention, the capacity region may not be convex, unlike in information theory where you can do time sharing.
- For wireless network coding it is important to connect the MAC protocol and scheduling issues as well as change the notion of cut capacities. That is, you shouldn’t replace edges with hyper-edges, because that’s not a good model.
- The information rate is the rate from the payload plus the information in the idleness and the information from the identity of the transmitter. That is, you get data from the actual packet, when the packet was sent, and who is sending the packet.
- Extending many analyses to more than 2 users has not been done.
- Can bursty traffic capacity be larger than non-bursty? The NNN (*) community says that would be a contradiction, because you can always then emulate bursty traffic. But this is unfair because idling the transmitter to build up packets and hence create artificial bursts is not allowed in the problem formulation, so there is no contradiction.
- Relaying is good from a network perspective because it can partially enable a first-come first-serve (FCFS) discipline. So relays bridge a gap to the optimal scheduling policy. This is different than the information theory notion of cooperation yielding diversity gain.
- Multicast throughput is an interesting thing to think about more rigorously for the future.
- His prescription : the information theory has to apply its tools more broadly to networking problems and to unorthodox problems. The networking community should use more rigorous modeling and analysis methods.
(*) NNN = Nagging nabobs of negativism (really it should be “nattering nabobs of negativism,” Safire’s famous alliterative phrase wielded with such gusto by Spiro Agnew).