A scratched disc still plays the whole track, and pictures from Voyager cross billions of kilometres and still assemble sharply, all because the data travels alongside redundancy computed in advance. A single parity bit only announces that something is wrong, never where. The Hamming (7,4) code plants three check bits so that when they disagree, the three values together spell out the position of the broken bit, which is then flipped back. Sending each bit three times and taking a majority also repairs errors, at the cost of two thirds of the bandwidth, while a burst of adjacent bad bits defeats a single-error code outright.
A scratched disc still plays the whole track, and pictures from Voyager cross billions of kilometres and still assemble sharply, all because the data travels alongside redundancy computed in advance. A single parity bit only announces that something is wrong, never where. The Hamming (7,4) code plants three check bits so that when they disagree, the three values together spell out the position of the broken bit, which is then flipped back. Sending each bit three times and taking a majority also repairs errors, at the cost of two thirds of the bandwidth, while a burst of adjacent bad bits defeats a single-error code outright.
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