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  2. Hamming code - Wikipedia

    en.wikipedia.org/wiki/Hamming_code

    It can correct one-bit errors or it can detect - but not correct - two-bit errors. A (4,1) repetition (each bit is repeated four times) has a distance of 4, so flipping three bits can be detected, but not corrected. When three bits flip in the same group there can be situations where attempting to correct will produce the wrong code word.

  3. Error correction code - Wikipedia

    en.wikipedia.org/wiki/Error_correction_code

    Turbo coding is an iterated soft-decoding scheme that combines two or more relatively simple convolutional codes and an interleaver to produce a block code that can perform to within a fraction of a decibel of the Shannon limit.

  4. Five-qubit error correcting code - Wikipedia

    en.wikipedia.org/wiki/Five-qubit_error...

    This page was last edited on 27 November 2024, at 15:25 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.

  5. Error detection and correction - Wikipedia

    en.wikipedia.org/wiki/Error_detection_and_correction

    A parity bit is a bit that is added to a group of source bits to ensure that the number of set bits (i.e., bits with value 1) in the outcome is even or odd. It is a very simple scheme that can be used to detect single or any other odd number (i.e., three, five, etc.) of errors in the output.

  6. Hamming (7,4) - Wikipedia

    en.wikipedia.org/wiki/Hamming(7,4)

    p 2 covers d 1, d 3, d 4; p 3 covers d 2, d 3, d 4; The remaining rows (3, 5, 6, 7) map the data to their position in encoded form and there is only 1 in that row so it is an identical copy. In fact, these four rows are linearly independent and form the identity matrix (by design, not coincidence). Also as mentioned above, the three rows of H ...

  7. Cross-interleaved Reed–Solomon coding - Wikipedia

    en.wikipedia.org/wiki/Cross-interleaved_Reed...

    In case the burst correction capability is exceeded, interpolation may provide concealment by approximation; Simple decoder strategy possible with reasonably-sized external random access memory; Very high efficiency; Room for future introduction of four audio channels without major changes in the format (as of 2024, this has not been implemented).

  8. 4B5B - Wikipedia

    en.wikipedia.org/wiki/4B5B

    For example, a run of 4 bits such as 0000 2 using NRZI encoding contains no transitions and that may cause clocking problems for the receiver. 4B5B solves this problem by assigning the 4-bit block a 5-bit code, in this case, 11110 2. There are eight 5-bit codes that have 3 consecutive 0s: 00000, 00001, 00010, 01000, 10000, 00011, 10001, 11000.

  9. Linear code - Wikipedia

    en.wikipedia.org/wiki/Linear_code

    A code is defined to be equidistant if and only if there exists some constant d such that the distance between any two of the code's distinct codewords is equal to d. [4] In 1984 Arrigo Bonisoli determined the structure of linear one-weight codes over finite fields and proved that every equidistant linear code is a sequence of dual Hamming ...

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