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  2. Error correction code - Wikipedia

    en.wikipedia.org/wiki/Error_correction_code

    If the number of errors within a code word exceeds the error-correcting code's capability, it fails to recover the original code word. Interleaving alleviates this problem by shuffling source symbols across several code words, thereby creating a more uniform distribution of errors. [ 21 ]

  3. Burst error-correcting code - Wikipedia

    en.wikipedia.org/wiki/Burst_error-correcting_code

    Proof. We need to prove that if you add a burst of length to a codeword (i.e. to a polynomial that is divisible by ()), then the result is not going to be a codeword (i.e. the corresponding polynomial is not divisible by ()).

  4. Hamming code - Wikipedia

    en.wikipedia.org/wiki/Hamming_code

    As explained earlier, it can either detect and correct single-bit errors or it can detect (but not correct) both single and double-bit errors. With the addition of an overall parity bit, it becomes the [8,4] extended Hamming code and can both detect and correct single-bit errors and detect (but not correct) double-bit errors.

  5. BCH code - Wikipedia

    en.wikipedia.org/wiki/BCH_code

    One of the key features of BCH codes is that during code design, there is a precise control over the number of symbol errors correctable by the code. In particular, it is possible to design binary BCH codes that can correct multiple bit errors.

  6. Concatenated error correction code - Wikipedia

    en.wikipedia.org/wiki/Concatenated_error...

    Similarly, the inner code can reliably correct an input y i if less than d/2 inner symbols are erroneous. Thus, for an outer symbol y' i to be incorrect after inner decoding at least d/2 inner symbols must have been in error, and for the outer code to fail this must have happened for at least D/2 outer symbols.

  7. Cyclic redundancy check - Wikipedia

    en.wikipedia.org/wiki/Cyclic_redundancy_check

    The concept of the CRC as an error-detecting code gets complicated when an implementer or standards committee uses it to design a practical system. Here are some of the complications: Sometimes an implementation prefixes a fixed bit pattern to the bitstream to be checked. This is useful when clocking errors might insert 0-bits in front of a ...

  8. Hamming (7,4) - Wikipedia

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

    Hamming's (7,4) algorithm can correct any single-bit error, or detect all single-bit and two-bit errors. In other words, the minimal Hamming distance between any two correct codewords is 3, and received words can be correctly decoded if they are at a distance of at most one from the codeword that was transmitted by the sender.

  9. Reed–Solomon error correction - Wikipedia

    en.wikipedia.org/wiki/Reed–Solomon_error...

    A Reed–Solomon code (like any MDS code) is able to correct twice as many erasures as errors, and any combination of errors and erasures can be corrected as long as the relation 2E + S ≤ n − k is satisfied, where is the number of errors and is the number of erasures in the block.