Information Theory Learning Path

Definition and scope of information theory

Information theory is the mathematical study of quantifying, storing, and communicating a mathematically defined type of information. Conceived by Claude Shannon in the 1940s, it treats information as a way to measure uncertainty: before a message is known, uncertainty is high, and after the message is observed, uncertainty decreases. A central example is a fair coin flip, where the initial uncertainty corresponds to 1 bit of information, and becomes 0 bits once the outcome is revealed. In Shannon’s probabilistic framework, information is modeled as a set of possible messages sent over a (possibly noisy) communication channel, with the goal of enabling reliable reconstruction at the receiver. This leads to foundational results such as the noisy-channel coding theorem, which links the maximum achievable information rate to the channel capacity determined by the channel’s statistical behavior. The scope of information theory therefore includes core measures of information (like entropy, mutual information, and related quantities), and the design of coding and communication methods for efficient data compression and error correction, with broad applications across mathematics, statistics, computer science, and engineering as well as fields such as cryptography, signal processing, and biology.

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Uncertainty as a model of information

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