Information Theory Learning Path

Definition and scope of information theory

Information theory is the mathematical study of how to quantify, store, and communicate a well-defined type of information. In Shannon’s probabilistic view, information can be understood as the resolution of uncertainty: before observing an event, uncertainty is high, and after observing it, uncertainty decreases. A central example is a fair coin flip, where the uncertainty before seeing the result is 1 bit (using a base-2 logarithm), and the uncertainty becomes 0 after the outcome is known. The scope of information theory includes defining and analyzing quantitative measures of information for probability distributions of random variables. Core quantities include entropy (uncertainty of a single source), joint entropy (uncertainty of paired variables), conditional entropy or equivocation (uncertainty remaining about one variable given another), and mutual information (how much observing one variable reduces uncertainty about the other). These measures underpin major results in communication and coding theory, such as the noisy-channel coding theorem and the idea of channel capacity, which characterize the maximum reliable communication rate based on channel statistics.

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Uncertainty as information resolution

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