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Information theory quantifies uncertainty and studies how information can be communicated reliably in the presence of noise using probabilistic models.
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.
Information theory quantifies uncertainty and studies how information can be communicated reliably in the presence of noise using probabilistic models.
Its scope covers fundamental measures like entropy, conditional entropy, joint entropy, and mutual information, which support results in coding and communication such as channel capacity.
A measure of the uncertainty (lack of information) associated with a probability distribution over outcomes.
The average uncertainty remaining about a random variable X after observing another random variable Y.
The uncertainty associated with the combined outcomes of two (or more) random variables treated together.
A measure of how much knowing one random variable reduces uncertainty about another, i.e., the shared information between them.
The maximum achievable reliable communication rate over a noisy channel, determined by the channel’s statistical properties.
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