Algorithmic Results in List Decoding

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Error-correcting codes are used to cope with the corruption of data by noise during communication or storage. A code uses an encoding procedure that judiciously introduces redundancy into the data to produce an associated codeword. The redundancy built into the codewords enables one to decode the original data even from a somewhat distorted version of the codeword. The central trade-off in coding theory is the one between the data rate (amount of non-redundant information per bit of codeword) and the error rate (the fraction of symbols that could be corrupted while still enabling data recovery). The traditional decoding algorithms did as badly at correcting any error pattern as they would do for the worst possible error pattern. This severely limited the maximum fraction of errors those algorithms could tolerate. In turn, this was the source of a big hiatus between the error-correction performance known for probabilistic noise models (pioneered by Shannon) and what was thought to be t...

Venkatesan Guruswami

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