In the
compact disc
The compact disc (CD) is a digital optical disc data storage format that was co-developed by Philips and Sony to store and play digital audio recordings. In August 1982, the first compact disc was manufactured. It was then released in O ...
system,
cross-interleaved Reed–Solomon code (CIRC) provides error detection and
error correction
In information theory and coding theory with applications in computer science and telecommunication, error detection and correction (EDAC) or error control are techniques that enable reliable delivery of digital data over unreliable communi ...
. CIRC adds to every three data
byte
The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable uni ...
s one
redundant parity
Parity may refer to:
* Parity (computing)
** Parity bit in computing, sets the parity of data for the purpose of error detection
** Parity flag in computing, indicates if the number of set bits is odd or even in the binary representation of the ...
byte.
Overview
Reed–Solomon codes are specifically useful in combating mixtures of random and burst
error
An error (from the Latin ''error'', meaning "wandering") is an action which is inaccurate or incorrect. In some usages, an error is synonymous with a mistake. The etymology derives from the Latin term 'errare', meaning 'to stray'.
In statistics ...
s. CIRC corrects
error burst
In telecommunication, a burst error or error burst is a contiguous sequence of symbols, received over a communication channel, such that the first and last symbols are in error and there exists no contiguous subsequence of ''m'' correctly receive ...
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 field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points.
In engineering and science, one often has ...
may provide concealment by approximation
* Simple decoder strategy possible with reasonably-sized external
random access memory
Random-access memory (RAM; ) is a form of computer memory that can be read and changed in any order, typically used to store working data and machine code. A random-access memory device allows data items to be read or written in almost the ...
* 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
compact disc
The compact disc (CD) is a digital optical disc data storage format that was co-developed by Philips and Sony to store and play digital audio recordings. In August 1982, the first compact disc was manufactured. It was then released in O ...
s (CDs) 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
concatenate
In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end. For example, the concatenation of "snow" and "ball" is "snowball". In certain formalisations of concatenat ...
d Reed–Solomon codes, which are interleaved cross-wise. Judicious positioning of the
stereo
Stereophonic sound, or more commonly stereo, is a method of sound reproduction that recreates a multi-directional, 3-dimensional audible perspective. This is usually achieved by using two independent audio channels through a configuration ...
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.
References
See also
*
Multiplexing
In telecommunications and computer networking, multiplexing (sometimes contracted to muxing) is a method by which multiple analog or digital signals are combined into one signal over a shared medium. The aim is to share a scarce resource - ...
*
Parity (mathematics)
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is a multiple of two, and odd if it is not.. For example, −4, 0, 82 are even because
\begin
-2 \cdot 2 &= -4 \\
0 \cdot 2 &= 0 \\
4 ...
*
Parity (telecommunication)
A parity bit, or check bit, is a bit added to a string of binary code. Parity bits are a simple form of error detecting code. Parity bits are generally applied to the smallest units of a communication protocol, typically 8-bit octets (bytes), ...
*
Checksum
A checksum is a small-sized block of data derived from another block of digital data for the purpose of detecting errors that may have been introduced during its transmission or storage. By themselves, checksums are often used to verify data ...
*
Error correction
In information theory and coding theory with applications in computer science and telecommunication, error detection and correction (EDAC) or error control are techniques that enable reliable delivery of digital data over unreliable communi ...
*
Reed–Solomon error correction
Reed–Solomon codes are a group of error-correcting codes that were introduced by Irving S. Reed and Gustave Solomon in 1960.
They have many applications, the most prominent of which include consumer technologies such as MiniDiscs, CDs, DVDs, ...
{{DEFAULTSORT:Cross-interleaved Reed-Solomon coding
Error detection and correction
Compact disc