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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 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.
In 1956, Claude Shannon introduced the discrete memoryless channel with noiseless feedback. In 1961, Alfréd Rényi introduced the Bar-Kochba game (also known as Twenty questions ), with a given percentage of wrong answers, and calculated the minimum number of randomly chosen questions to determine the answer.
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 ...
Learn about the techniques and methods to ensure reliable delivery of digital data over unreliable communication channels. Find out the definitions, history ...
Learn about the methods and codes to correct burst errors, which are errors that occur in many consecutive bits. Find definitions, examples, theorems and algorithms for cyclic codes and burst descriptions.