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  2. 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 ...

  3. Noisy-channel coding theorem - Wikipedia

    en.wikipedia.org/wiki/Noisy-channel_coding_theorem

    Stated by Claude Shannon in 1948, the theorem describes the maximum possible efficiency of error-correcting methods versus levels of noise interference and data corruption. Shannon's theorem has wide-ranging applications in both communications and data storage. This theorem is of foundational importance to the modern field of information theory ...

  4. Shannon–Hartley theorem - Wikipedia

    en.wikipedia.org/wiki/Shannon–Hartley_theorem

    [6] [7] The proof of the theorem shows that a randomly constructed error-correcting code is essentially as good as the best possible code; the theorem is proved through the statistics of such random codes. Shannon's theorem shows how to compute a channel capacity from a statistical description of a channel, and establishes that given a noisy ...

  5. Information theory - Wikipedia

    en.wikipedia.org/wiki/Information_theory

    Download QR code; Print/export ... Shannon's source coding theorem; ... In Shannon's revolutionary and groundbreaking paper, the work for which had been substantially ...

  6. Entropy coding - Wikipedia

    en.wikipedia.org/wiki/Entropy_coding

    More precisely, the source coding theorem states that for any source distribution, the expected code length satisfies ⁡ [(())] ⁡ [⁡ (())], where is the number of symbols in a code word, is the coding function, is the number of symbols used to make output codes and is the probability of the source symbol. An entropy coding attempts to ...

  7. Shannon coding - Wikipedia

    en.wikipedia.org/wiki/Shannon_coding

    The method was the first of its type, the technique was used to prove Shannon's noiseless coding theorem in his 1948 article "A Mathematical Theory of Communication", [1] and is therefore a centerpiece of the information age.

  8. Channel capacity - Wikipedia

    en.wikipedia.org/wiki/Channel_capacity

    Shannon's source coding theorem; ... (SNR). This result is known as the Shannon–Hartley theorem. [11] ... code is a pair of encoding and decoding mappings with = ...

  9. A Mathematical Theory of Communication - Wikipedia

    en.wikipedia.org/wiki/A_Mathematical_Theory_of...

    Shannon's diagram of a general communications system, showing the process by which a message sent becomes the message received (possibly corrupted by noise) This work is known for introducing the concepts of channel capacity as well as the noisy channel coding theorem. Shannon's article laid out the basic elements of communication: