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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.
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.
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.
Learn about forward error correction (FEC) or channel coding, a technique for controlling errors in data transmission over unreliable or noisy channels. FEC adds ...
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.
Learn about the limits of data compression for independent and identically-distributed random variables, and the role of Shannon entropy. See the statements, proofs and extensions of the source coding theorem for symbol codes and non-stationary sources.
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 ...
The entanglement-assisted classical capacity theorem is proved in two parts: the direct coding theorem and the converse theorem. The direct coding theorem demonstrates that the quantum mutual information of the channel is an achievable rate, by a random coding strategy that is effectively a noisy version of the super-dense coding protocol. The ...