In the
compact discA Compact Disc is an optical disc used to store digital data. It was originally developed to store sound recordings exclusively, but later it also allowed the preservation of other types of data. Audio CDs have been commercially available since October 1982...
system, error correction and detection is provided by
cross-interleavedIn computer science, interleaving is a way to arrange data in a non-contiguous way to increase performance.It is used in:* In telecommunications: time-division multiplexing , data transmission, error correction* computer memory* disk storage...
Reed-Solomon code. CIRC adds to every three data
byteA byte is a unit of information storage representing the smallest addressable element for a given computer architecture. It often designates a sequence of bits whose length is determined by the architecture...
s one
redundantRedundancy in information theory is the number of bits used to transmit a message minus the number of bits of actual information in the message. Informally, it is the amount of wasted "space" used to transmit certain data...
parityA parity bit is a bit that is added to ensure that the number of bits with the value one in a set of bits is even or odd. Parity bits are used as the simplest form of error detecting code....
byte.
Reed-Solomon codes are specifically useful in combating mixtures of random and burst
errorThe word error has different meanings and usages relative to how it is conceptually applied. The concrete meaning of the Latin word error is "wandering" or "straying". To the contrary of an illusion, an error or a mistake can sometimes be dispelled through knowledge...
s. CIRC corrects
error burstIn telecommunication, an error burst is a contiguous sequence of symbols, received over a data transmission channel, such that the first and last symbols are in error and there exists no contiguous subsequence of m correctly received symbols within the error burst.The integer parameter m is...
s 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.
- High random error correctability
- Long burst error correctability
- In case the burst correction capability is exceeded, interpolation
In the mathematical subfield of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points....
may provide concealment by approximation
- Simple decoder
A decoder is a device which does the reverse of an encoder, undoing the encoding so that the original information can be retrieved. The same method used to encode is usually just reversed in order to decode....
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).
Errors found in the CD system are a combination of random and burst errors.
Discussion
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In the
compact discA Compact Disc is an optical disc used to store digital data. It was originally developed to store sound recordings exclusively, but later it also allowed the preservation of other types of data. Audio CDs have been commercially available since October 1982...
system, error correction and detection is provided by
cross-interleavedIn computer science, interleaving is a way to arrange data in a non-contiguous way to increase performance.It is used in:* In telecommunications: time-division multiplexing , data transmission, error correction* computer memory* disk storage...
Reed-Solomon code. CIRC adds to every three data
byteA byte is a unit of information storage representing the smallest addressable element for a given computer architecture. It often designates a sequence of bits whose length is determined by the architecture...
s one
redundantRedundancy in information theory is the number of bits used to transmit a message minus the number of bits of actual information in the message. Informally, it is the amount of wasted "space" used to transmit certain data...
parityA parity bit is a bit that is added to ensure that the number of bits with the value one in a set of bits is even or odd. Parity bits are used as the simplest form of error detecting code....
byte.
Overview
Reed-Solomon codes are specifically useful in combating mixtures of random and burst
errorThe word error has different meanings and usages relative to how it is conceptually applied. The concrete meaning of the Latin word error is "wandering" or "straying". To the contrary of an illusion, an error or a mistake can sometimes be dispelled through knowledge...
s. CIRC corrects
error burstIn telecommunication, an error burst is a contiguous sequence of symbols, received over a data transmission channel, such that the first and last symbols are in error and there exists no contiguous subsequence of m correctly received symbols within the error burst.The integer parameter m is...
s 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.
Characteristics
- High random error correctability
- Long burst error correctability
- In case the burst correction capability is exceeded, interpolation
In the mathematical subfield of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points....
may provide concealment by approximation
- Simple decoder
A decoder is a device which does the reverse of an encoder, undoing the encoding so that the original information can be retrieved. The same method used to encode is usually just reversed in order to decode....
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
stereoStereophonic sound, commonly called stereo, is the reproduction of sound using two or more independent audio channels through a symmetrical configuration of loudspeakers in such a way as to create the impression of sound heard from various directions, as in natural hearing...
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.
See also
- interleaving
In computer science, interleaving is a way to arrange data in a non-contiguous way to increase performance.It is used in:* In telecommunications: time-division multiplexing , data transmission, error correction* computer memory* disk storage...
- multiplexing
The multiplexed signal is transmitted over a communication channel, which may be a physical transmission medium. The multiplexing divides the capacity of the low-level communication channel into several higher-level logical channels, one for each message signal or data stream to be transferred...
- parity (mathematics)
- parity (telecommunication)
- checksum
A checksum or hash sum is a fixed-size datum computed from an arbitrary block of digital data for the purpose of detecting accidental errors that may have been introduced during its transmission or storage. The integrity of the data can be checked at any later time by recomputing the checksum and...
- Error correction
- Reed–Solomon error correction
Reed–Solomon error correction is an error-correcting code that works by oversampling a polynomial constructed from the data. The polynomial is evaluated at several points, and these values are sent or recorded. Sampling the polynomial more often than is necessary makes the polynomial over-determined...