Reed-Solomon (RS) is a method of error correcting encoding used for high integrity data communications through a noisy channel. RS works by oversampling a polynomial constructed from the data which is being encoded. By sending the coefficients of the oversampled polynomial, it is possible to decode the information present even if errors or omissions occur, due to the noisy channel.
RS, like most error correcting codes, may both detect and correct errors. RS may also correct omissions. Many other forms of error correcting encoding, such as a Hamming code, may also detect and correct for limited errors in data, as RS does. The degenerate case of error correcting codes, a simple parity bit, is unable to correct errors but is able to detect single bit errors.
By contrast, RS is able to detect and correct up to (n-k)/2 errors, that is up to half off the amount of oversampling, in errors. In example, if I transmit a 64 symbol RS code block, generated from a 32 symbol data stream, I would be able to correct 16 possible symbol errors and/or omissions.
RS has many applications in the modern world. The most common application where RS is used is found in compact discs. a RS code is used to encoded the data being burned into a CD. When the data is read off of the CD, errors and omissions caused by oily fingerprints and/or scratches are corrected in the decoding process. Without some form of error correcting coding, such as RS, CD's would be unplayable, as the smallest particle of dirt, the tiniest scratch, would corrupt the data being read off of the CD. This would result in corrupted data, skips, crackles and pops in music.
Another wide use of RS is in spacecraft. Spacecraft, such as the Voyager probes, must transmit vital data through extremely noisy channels. The data being transmitted is also being received at an extremely low power density, increasing the signal to noise ratio (SNR). Both of these factors make the reception of error-free data extremely unlikely. Thus, extremely error-tolerant error correcting codes, such as RS, are needed.
More information may be found at wikipedia