I’ve been meaning to write some notes towards a contextualization of the research I’ve been doing lately, as part of an effort to find a better angle on things and also spur myself to actually tackle some harder/more interesting problems than I’ve looked at so far. At the moment I’m looking at communication scenarios in which there is some unknown interference. The crux of the matter is that the communication strategy must be designed knowing that the interference is there, but not what it is like. There is a disconnect between two different strands of research on this subject (so much so that the papers in one don’t cite the other as relevant). In both the interference is viewed as coming from a jammer who wants to screw over your communication.
In the world of arbitrarily varying channels (Blackwell, Breiman and Thomasian, Ahlswede, Csiszar and Narayan, Hughes and Narayan, etc), mostly populated by mathematicians, interference is treated as malicious but not listening in. Perhaps a better way to view it is that you want to provide guarantees even if the interference behaves in the worst way possible. This worst-case analysis is often no different from the case when you have a statistical description of the analysis — the average and worst-case scenarios are quite similar. However, in some situations the worst-case is significantly worse than the average case. Here, if a secret key is shared between the transmitter and receiver, we can recover the average-case behavior, although the reliabiliity of the communication may be worse.
On the other side, we have wire-tap situations in which the jammer not only knows your encoding scheme, but also can try to figure out what you’re sending and actively cancel it out. Most of these analyses initially took the form of game-theory set-ups in which one player tries to maximize a function (the capacity) and the other tries to minimize it. The space of strategies for each player take the form of choosing probability distributions. In this highly structured framework you can prove minimax theories about the jammer and and encoder strategies. Extensions to this view take into account channel fading for wireless, or interference for multiple access (Shafiee and Ulukus).
But never the twain shall meet, as Kipling would say, and it’s hard to sort out the connections between interference, jamming, statistical knowledge, and robustness. Part of what I have to do is sort out what is what and see if I can make any more statements stitching the two together and finding real scenarios in which the unreasonableness of the models can be made more reasonable.