Local Decoding and Testing of Codes
Sometimes it is only necessary to decode single bits of the message, or to check whether a given signal is a codeword, and do so without looking at the entire signal. This can make sense in a streaming setting, where codewords are too large to be classically decoded fast enough and where only a few bits of the message are of interest for now. Also such codes have become an important tool in computational complexity theory, e.g., for the design of probabilistically checkable proofs.
Locally decodable codes are error-correcting codes for which single bits of the message can be probabilistically recovered by only looking at a small (say constant) number of positions of a codeword, even after the codeword has been corrupted at some constant fraction of positions. Locally testable codes are error-correcting codes for which it can be checked probabilistically whether a signal is close to a codeword by only looking at a small number of positions of the signal.
Read more about this topic: Forward Error Correction
Famous quotes containing the words local, testing and/or codes:
“Reporters for tabloid newspapers beat a path to the park entrance each summer when the national convention of nudists is held, but the cult’s requirement that visitors disrobe is an obstacle to complete coverage of nudist news. Local residents interested in the nudist movement but as yet unwilling to affiliate make observations from rowboats in Great Egg Harbor River.”
—For the State of New Jersey, U.S. public relief program (1935-1943)
“Now I see that going out into the testing ground of men it is the tongue and not the deed that wins the day.”
—Sophocles (497–406/5 B.C.)
“Thou hast a voice, great Mountain, to repeal
Large codes of fraud and woe; not understood
By all, but which the wise, and great, and good
Interpret, or make felt, or deeply feel.”
—Percy Bysshe Shelley (1792–1822)