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It has tens of thousands of citations, being one of the most influential and cited scientific papers of all time, [6] as it gave rise to the field of information theory, with Scientific American referring to the paper as the "Magna Carta of the Information Age", [7] while the electrical engineer Robert G. Gallager called the paper a "blueprint ...
Here, () = = is the entropy, and Shannon's source coding theorem says that any code must have an average length of at least (). Hence we see that the Shannon–Fano code is always within one bit of the optimal expected word length.
The Shannon–Weaver model is one of the first models of communication. Initially published in the 1948 paper "A Mathematical Theory of Communication", it explains communication in terms of five basic components: a source, a transmitter, a channel, a receiver, and a destination. The source produces the original message.
In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise contamination of a communication channel, it is possible (in theory) to communicate discrete data (digital information) nearly error-free up to a computable maximum rate through the channel.
In information theory, the source coding theorem (Shannon 1948) [2] informally states that (MacKay 2003, pg. 81, [3] Cover 2006, Chapter 5 [4]): N i.i.d. random variables each with entropy H(X) can be compressed into more than N H(X) bits with negligible risk of information loss, as N → ∞; but conversely, if they are compressed into fewer than N H(X) bits it is virtually certain that ...
Łoś' theorem (model theory) Lovelock's theorem ; Löwenheim–Skolem theorem (mathematical logic) Lucas's theorem (number theory) Lukacs's proportion-sum independence theorem (probability) Lumer–Phillips theorem (semigroup theory) Luzin's theorem (real analysis) Lyapunov–Malkin theorem (stability theory)
Leslie B. Lamport (born February 7, 1941) is an American computer scientist and mathematician.Lamport is best known for his seminal work in distributed systems, and as the initial developer of the document preparation system LaTeX and the author of its first manual.
Let : where we assume in the typical case that = = {,} and = {,}.Alice holds an -bit string while Bob holds an -bit string .By communicating to each other one bit at a time (adopting some communication protocol which is agreed upon in advance), Alice and Bob wish to compute the value of (,) such that at least one party knows the value at the end of the communication.