Cross-Interleaved Reed-Solomon Coding
Encyclopedia
In the compact disc
system, cross-interleaved
Reed-Solomon code (or CIRC) provides error detection and error correction. CIRC adds to every three data byte
s one redundant
parity
byte.
s. CIRC corrects error burst
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.
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.
Compact Disc
The Compact Disc is an optical disc used to store digital data. It was originally developed to store and playback sound recordings exclusively, but later expanded to encompass data storage , write-once audio and data storage , rewritable media , Video Compact Discs , Super Video Compact Discs ,...
system, cross-interleaved
Interleaving
In computer science and telecommunication, interleaving is a way to arrange data in a non-contiguous way to increase performance.It is typically used:* In error-correction coding, particularly within data transmission, disk storage, and computer memory....
Reed-Solomon code (or CIRC) provides error detection and error correction. CIRC adds to every three data byte
Byte
The byte is a unit of digital information in computing and telecommunications that most commonly consists of eight bits. Historically, a byte was the number of bits used to encode a single character of text in a computer and for this reason it is the basic addressable element in many computer...
s one redundant
Redundancy (information theory)
Redundancy 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...
parity
Parity bit
A 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 errorError
The word error entails different meanings and usages relative to how it is conceptually applied. The concrete meaning of the Latin word "error" is "wandering" or "straying". Unlike an illusion, an error or a mistake can sometimes be dispelled through knowledge...
s. CIRC corrects error burst
Error burst
In telecommunication, a burst error or 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...
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, interpolationInterpolationIn the mathematical field 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 decoderDecoderA decoder is a device which does the reverse operation 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
The term Stereophonic, commonly called stereo, sound refers to any method of sound reproduction in which an attempt is made to create an illusion of directionality and audible perspective...
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.
See also
- interleavingInterleavingIn computer science and telecommunication, interleaving is a way to arrange data in a non-contiguous way to increase performance.It is typically used:* In error-correction coding, particularly within data transmission, disk storage, and computer memory....
- multiplexingMultiplexingThe 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)
- checksumChecksumA 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 correctionReed–Solomon error correctionIn coding theory, Reed–Solomon codes are non-binary cyclic error-correcting codes invented by Irving S. Reed and Gustave Solomon. They described a systematic way of building codes that could detect and correct multiple random symbol errors...