Separation theorems and partial orderings for sensor network problems

In the absence of complexity and delay constraints, the quality of a noisy communication channel can be characterized by a single number, called its capacity and usually measured in bits. Shannon [1] showed that this number is universal in the sense that via the so-called source/channel separation theorem, it applies to all (stationary, ergodic) communication problems, making bits the universal currency of information in point-to-point communication. More explicitly, the potential offered by a noisy communication channel is fully characterized by its capacity, and the difficulty of communicating a source (in general, with respect to a distortion criterion) is fully characterized by its rate-distortion function.