Coding Theorems and Weight of Evidence

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Abstract
Proofs of some coding theorems, somewhat more general than Shannon's Fundamental Theorem, are given in outline in terms of “weights of evidence” (logarithms of Bayes factors). Although the approach is not intended to be entirely rigorous, it shows how the concept of amount of information arises as a very close approximation to weight of evidence when “random coding” is used; it makes the intuitive idea of some coding theorems unusually clear; and it provides information concerning the message length required for a given probability of error. Our discussion is almost entirely restricted to the case of discrete channels without memory.

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