Cross-interleaved Reed-Solomon coding


Cross-interleaved Reed-Solomon coding

In the compact disc system, error correction and detection is provided by cross-interleaved Reed-Solomon code. [US patent|4,413,340, CIRC Patent] CIRC adds to every three data bytes one redundant parity byte.

Overview

Reed-Solomon codes are specifically useful in combating mixtures of random and burst errors. CIRC corrects error bursts up to 3,500 bits in sequence (2.4 mm in length as seen on CD surface) and compensates for error bursts up to 12,000 bits (8.5 mm) that may be caused by minor scratches. [K.A.S. Immink, "Reed-Solomon Codes and the Compact Disc" in S.B. Wicker and V.K. Bhargava, Edrs, "Reed-Solomon Codes and Their Applications", IEEE Press, 1994.]

Characteristics

* High random error correctability
* Long burst error correctability
* In case the burst correction capability is exceeded, interpolation may provide concealment by approximation
* Simple decoder strategy possible with reasonably-sized external random access memory
* Very high efficiency
* Room for future introduction of four audio channels without major changes in the format (as of 2008, this has not been implemented).

Interleave

Errors found in the CD system are a combination of random and burst errors. In order to alleviate the strain on the error control code, some form of interleaving is required. The CD system employs two concatenated Reed-Solomon codes, which are interleaved cross-wise. Judicious positioning of the stereo channels as well as the audio samples on even or odd-number instants within the interleaving scheme provide the error concealment ability, and the multitude of interleave structures used on the CD makes it possible to correct and detect errors with a relatively low amount of redundancy.

Interpolation

If a major error occurs and a sample cannot be perfectly reconstructed by the error control circuitry, it is possible to "guess" the content of the sample; that is, obtain an approximation by interpolating it off the neighbouring audio samples. While this concealment will not "fix" the error, it will make it inaudible, offering a graceful degradation of audio quality as clicks and pops are avoided.

References

ee also

*interleaving
*multiplexing
*parity (mathematics)
*parity (telecommunication)
*checksum
*Error correction
*Reed–Solomon error correction


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