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Learn about the Shannon limit or Shannon capacity of a communication channel, which is the maximum rate of error-free data that can be transmitted over a noisy channel. The theorem was proved by Claude Shannon in 1948 and has wide applications in information theory and data storage.
Learn about forward error correction (FEC) or channel coding, a technique for controlling errors in data transmission over unreliable or noisy channels. FEC adds ...
On-line textbook: Information Theory, Inference, and Learning Algorithms, by David MacKay - gives an entertaining and thorough introduction to Shannon theory, including two proofs of the noisy-channel coding theorem. This text also discusses state-of-the-art methods from coding theory, such as low-density parity-check codes, and Turbo codes.
The Shannon–Hartley theorem is a special case of the noisy-channel coding theorem that applies to an additive white Gaussian noise (AWGN) channel. It states that the channel capacity is proportional to the logarithm of the signal-to-noise ratio and the bandwidth.
Forney constructed a concatenated code = to achieve the capacity of the noisy-channel coding theorem for . In his code, In his code, The outer code C out {\displaystyle C_{\text{out}}} is a code of block length N {\displaystyle N} and rate 1 − ϵ 2 {\displaystyle 1-{\frac {\epsilon }{2}}} over the field F 2 k {\displaystyle F_{2^{k}}} , and k ...
An error-correcting code is a way of encoding x as a message such that Bob will successfully understand the value x as intended by Alice, even if the message Alice sends and the message Bob receives differ. In an error-correcting code with feedback, the channel is two-way: Bob can send feedback to Alice about the message he received.
Information theory is the mathematical study of the quantification, storage, and communication of information. It was established by Claude Shannon in the 1940s and has applications in various fields, such as coding, cryptography, neurobiology, and physics.
Learn about the 1948 article by Claude E. Shannon that founded the field of information theory and introduced the concepts of channel capacity, entropy, redundancy and bit. The article also proposed the Shannon–Fano coding technique and was later published as a book in 1949.