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  2. Coding theory - Wikipedia

    en.wikipedia.org/wiki/Coding_theory

    The decisive event which established the discipline of information theory, and brought it to immediate worldwide attention, was the publication of Claude E. Shannon's classic paper "A Mathematical Theory of Communication" in the Bell System Technical Journal in July and October 1948.

  3. Information theory - Wikipedia

    en.wikipedia.org/wiki/Information_theory

    This division of coding theory into compression and transmission is justified by the information transmission theorems, or source–channel separation theorems that justify the use of bits as the universal currency for information in many contexts.

  4. Block code - Wikipedia

    en.wikipedia.org/wiki/Block_code

    In coding theory, block codes are a large and important family of error-correcting codes that encode data in blocks. There is a vast number of examples for block codes, many of which have a wide range of practical applications.

  5. Shannon's source coding theorem - Wikipedia

    en.wikipedia.org/wiki/Shannon's_source_coding...

    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 ...

  6. Shannon–Fano coding - Wikipedia

    en.wikipedia.org/wiki/Shannon–Fano_coding

    Unfortunately, Shannon–Fano coding does not always produce optimal prefix codes; the set of probabilities {0.35, 0.17, 0.17, 0.16, 0.15} is an example of one that will be assigned non-optimal codes by Shannon–Fano coding. Fano's version of Shannon–Fano coding is used in the IMPLODE compression method, which is part of the ZIP file format ...

  7. Singleton bound - Wikipedia

    en.wikipedia.org/wiki/Singleton_bound

    In coding theory, the Singleton bound, named after Richard Collom Singleton, is a relatively crude upper bound on the size of an arbitrary block code with block length , size and minimum distance . It is also known as the Joshibound [ 1 ] proved by Joshi (1958) and even earlier by Komamiya (1953) .

  8. Decoding methods - Wikipedia

    en.wikipedia.org/wiki/Decoding_methods

    In coding theory, decoding is the process of translating received messages into codewords of a given code. There have been many common methods of mapping messages to codewords. These are often used to recover messages sent over a noisy channel, such as a binary symmetric channel.

  9. Shannon–Hartley theorem - Wikipedia

    en.wikipedia.org/wiki/Shannon–Hartley_theorem

    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.