---
title: "Information theory"
chunk: 1/7
source: "https://en.wikipedia.org/wiki/Information_theory"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:56:37.735412+00:00"
instance: "kb-cron"
---

Information theory is the mathematical study of the quantification, storage, and communication of a particular type of mathematically defined information. The field was established and formalized by Claude Shannon in the 1940s, though early contributions were made in the 1920s through the works of Harry Nyquist and Ralph Hartley. 
Information theory was initially formed in the context of telecommunication but soon found a wide range of other applications. It is now at the intersection of mathematics, statistics and computer science, and has applications in diverse fields ranging from electrical engineering and physics to neurobiology.
As a simple example of the concept, if one flips a fair coin and does not yet know the outcome (heads or tails), then they lack a certain amount of information. After looking at the coin, they gain information about the outcome. For a fair coin, the probability of either heads or tails is 1/2 and the amount of information is expressed as 
  
    
      
        −
        
          log
          
            2
          
        
        ⁡
        (
        1
        
          /
        
        2
        )
      
    
    {\displaystyle -\log _{2}(1/2)}
  
 = 1 bit of information.
A key concept in information theory is information entropy. In Shannon's formulation entropy is equal to the lack of information about an event. In the above coin flip example, the entropy in the case where you don't know the outcome is 1 bit. When you know the outcome after the coin has landed, the entropy is zero because you have gained one bit 
Information theory has been used in a wide range of applications, such as source coding/data compression (e.g. for ZIP files), and channel coding/error detection and correction (e.g. for DSL). Its impact has been crucial to the success of the Voyager missions to deep space, the invention of the compact disc, the feasibility of mobile phones and the development of the Internet and artificial intelligence. The theory has also found applications in other areas, including statistical inference, cryptography, neurobiology, perception, signal processing, linguistics, the evolution and function of molecular codes (bioinformatics), thermal physics, molecular dynamics, black holes, quantum computing, information retrieval, intelligence gathering, plagiarism detection, pattern recognition, anomaly detection, the analysis of music, art creation, imaging system design, study of outer space, the dimensionality of space, and epistemology.

== Overview ==
Information theory, as conceived by Claude Shannon, studies the processing and utilization of information within a probabilistic context. Abstractly, in this approach information can be thought of as the resolution of uncertainty. In the case of communication of information over a noisy channel, this abstract concept was formalized in 1948 by Claude Shannon in a paper entitled A Mathematical Theory of Communication, in which information is thought of as a set of possible messages, and the goal is to send these messages over a noisy channel, and to have the receiver reconstruct the message with low probability of error, in spite of the channel noise. Shannon's main result, the noisy-channel coding theorem, showed that, in the limit of many channel uses, the rate of information that is asymptotically achievable is equal to the channel capacity, a quantity dependent merely on the statistics of the channel over which the messages are sent.
Coding theory is concerned with finding explicit methods, called codes, for increasing the efficiency and reducing the error rate of data communication over noisy channels to near the channel capacity. These codes can be roughly subdivided into data compression (source coding) and error-correction (channel coding) techniques. In the latter case, it took many years to find the methods Shannon's work proved were possible.
A third class of information theory codes are cryptographic algorithms (both codes and ciphers). Concepts, methods and results from coding theory and information theory are widely used in cryptography and cryptanalysis, such as the unit ban.

== Historical background ==