Introduction to communication theory

Abstract

We noted in Chapter 11 that one of the motivations behind this work was the attempt to see Gibbsian statistical mechanics and Shannon's communication theory as examples of the same line of reasoning. A generalized form of statistical mechanics appeared as soon as we introduced the notion of entropy, and we ought now to be in a position to treat communication theory in a similar way. One difference is that in statistical mechanics the prior information has nothing to do with frequencies (it consists of measured values of macroscopic quantities such as pressure), and so we have little temptation to commit errors. But in communication theory the prior information consists, typically, of frequencies; this makes the probability – frequency conceptual pitfalls much more acute. For this reason it seemed best to take up communication theory only after we had seen the general connections between probability and frequency, in a variety of conceptually simpler applications. Origins of the theory Firstly, the difficult matter of giving credit where credit is due. All major advances in understanding have their precursors, whose full significance is never recognized at the time. Relativity theory had them in the work of Mach, Fitzgerald, Lorentz and Poincare, to mention only the most obvious examples. Communication theory had many precursors, in the work of Gibbs, Nyquist, Hartley, Szilard, von Neumann, and Wiener. But there is no denying that the work of Shannon (1948) represents the arrival of the main signal, just as did Einstein's of 1905.