A Mathematical Theory of Communication
đź“ś Abstract
The present paper deals with the problem of reproducing at one point either exactly or approximately a message selected at another point. Frequently the messages have meaning; that is they refer to or are correlated according to some system with certain physical or conceptual entities. These semantic aspects of communication are irrelevant to the engineering problem. The significant aspect is that the actual message is one selected from a set of possible messages. The system must be designed to operate for each potential selection, not just the one which will actually be chosen since this is unknown at the time of design. If the number of messages in the set is finite then this number or any monotonic function of this number can be regarded as a measure of the information produced when one message is chosen from the set, all choices being equally likely. As we shall see, the logarithmic function is more suitable for various reasons, both of a theoretical and practical nature.
✨ Summary
Claude E. Shannon’s paper, “A Mathematical Theory of Communication,” published in 1948, is a seminal work that founded the field of information theory. In this paper, Shannon introduces concepts such as entropy, which quantifies information, and discusses the capacity of communication channels, accounting for noise. The work underpins numerous fields including telecommunications, computer science, and data compression by formalizing the processes involved in transmitting information reliably and efficiently. Shannon’s model abstracts communication to its core components, laying the groundwork for the development of modern communication systems and compression algorithms.
This paper has fundamentally influenced various technical domains, and its concepts remain critical in designing digital communication systems and networks. For instance, it has significantly affected error detection and correction techniques, contributing to the robustness of digital data transmission in contemporary computing and networking industries. Furthermore, information theory principles are crucial in cryptography, data encryption, and compression.
Prominent references include:
- Cover, T. M., & Thomas, J. A. (2006). “Elements of Information Theory.” Wiley-Interscience. Link to reference
- MacKay, D. J. C. (2003). “Information Theory, Inference, and Learning Algorithms.” Cambridge University Press. Link to reference
- Pierce, J. R. (1980). “An Introduction to Information Theory: Symbols, Signals, & Noise.” Dover Publications.
- Gallager, R. G. (1968). “Information Theory and Reliable Communication.” Wiley.
- Shannon, C. E., & Weaver, W. (1963). “The Mathematical Theory of Communication.” University of Illinois Press. Link to reference
These works exhibit the profound and extensive impact of Shannon’s “A Mathematical Theory of Communication” on both theoretical and practical applications.