Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Formulated primarily by Claude E. Shannon in his 1948 paper “A Mathematical Theory of Communication,” information theory provides the foundation for modern digital communication and data compression techniques. Here are its key concepts:
- Entropy: A measure of the unpredictability or randomness of a source of information. It quantifies the average amount of information produced by a stochastic source of data.
- Redundancy: The difference between the entropy of a source and the average length of codes generated for that source. In communication, redundancy can be useful to detect and correct errors.
- Data Compression: Information theory provides the limits for how much a data set can be compressed without loss. Huffman coding and Lempel-Ziv-Welch (LZW) are examples of algorithms derived from this.
- Channel Capacity: The highest rate at which information can be sent through a communication channel without error given a specific level of noise. The Shannon-Hartley theorem gives the maximum rate of data transmission for a noisy channel.
- Coding Theory: Studies the properties and design of codes that are used to represent data. Error-correcting codes can be used to detect and correct errors in data transmission.
- Mutual Information: Measures the amount of information shared between two random variables. It quantifies the reduction in uncertainty about one variable given the knowledge of the other.
- Noise: Random interference or disturbances that can affect the transmission of a message. Information theory explores how to transmit data reliably in the presence of noise.
- Source Coding: The representation of data from a source with fewer bits, i.e., compressing the data.
- Channel Coding: Adding redundancy to data before transmission to ensure that it can be correctly decoded after being sent through a noisy channel.
- Rate-Distortion Theory: Deals with the trade-off between the fidelity (accuracy) of a reconstructed signal and the rate at which it’s represented.
Information theory has applications in various fields, including telecommunications, computer science, cryptography, neuroscience, and even quantum physics. Its principles are foundational to the design and operation of modern digital communication systems and storage solutions.