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Cross-interleaved Reed–Solomon Coding
In the compact disc system, cross-interleaved Reed–Solomon code (CIRC) provides error detection and error correction. 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. 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 compact discs (CDs) are a combin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compact Disc
The compact disc (CD) is a Digital media, 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 October 1982 in Japan and branded as ''Compact Disc Digital Audio, Digital Audio Compact Disc''. The format was later adapted (as CD-ROM) for general-purpose data storage. Several other formats were further derived, including write-once audio and data storage (CD-R), rewritable media (CD-RW), Video CD (VCD), Super Video CD (SVCD), Photo CD, Picture CD, Compact Disc-Interactive (CD-i) and Enhanced Music CD. Standard CDs have a diameter of and are designed to hold up to 74 minutes of uncompressed stereo digital audio or about 650 mebibyte, MiB of data. Capacity is routinely extended to 80 minutes and 700 mebibyte, MiB by arranging data more closely on the same sized disc. The Mini CD has various diameters ranging from ; t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 (computing), data and machine code. A Random access, random-access memory device allows data items to be read (computer), read or written in almost the same amount of time irrespective of the physical location of data inside the memory, in contrast with other direct-access data storage media (such as hard disks, CD-RWs, DVD-RWs and the older Magnetic tape data storage, magnetic tapes and drum memory), where the time required to read and write data items varies significantly depending on their physical locations on the recording medium, due to mechanical limitations such as media rotation speeds and arm movement. RAM contains multiplexer, multiplexing and demultiplexing circuitry, to connect the data lines to the addressed storage for reading or writing the entry. Usually more than one bit of storage is accessed by the same address, and RAM ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 communication channels. Many communication channels are subject to channel noise, and thus errors may be introduced during transmission from the source to a receiver. Error detection techniques allow detecting such errors, while error correction enables reconstruction of the original data in many cases. Definitions ''Error detection'' is the detection of errors caused by noise or other impairments during transmission from the transmitter to the receiver. ''Error correction'' is the detection of errors and reconstruction of the original, error-free data. History In classical antiquity, copyists of the Hebrew Bible were paid for their work according to the number of stichs (lines of verse). As the prose books of the Bible were hardly ever wr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 integrity but are not relied upon to verify data authenticity. The procedure which generates this checksum is called a checksum function or checksum algorithm. Depending on its design goals, a good checksum algorithm usually outputs a significantly different value, even for small changes made to the input. This is especially true of cryptographic hash functions, which may be used to detect many data corruption errors and verify overall data integrity; if the computed checksum for the current data input matches the stored value of a previously computed checksum, there is a very high probability the data has not been accidentally altered or corrupted. Checksum functions are related to hash functions, fingerprints, randomization functions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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), although they can also be applied separately to an entire message string of bits. The parity bit ensures that the total number of 1-bits in the string is even or odd. Accordingly, there are two variants of parity bits: even parity bit and odd parity bit. In the case of even parity, for a given set of bits, the bits whose value is 1 are counted. If that count is odd, the parity bit value is set to 1, making the total count of occurrences of 1s in the whole set (including the parity bit) an even number. If the count of 1s in a given set of bits is already even, the parity bit's value is 0. In the case of odd parity, the coding is reversed. For a given set of bits, if the count of bits with a value of 1 is even, the parity bit value is set ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 \\ 41 \cdot 2 &= 82 \end By contrast, −3, 5, 7, 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers like 1/2 or 4.201. See the section "Higher mathematics" below for some extensions of the notion of parity to a larger class of "numbers" or in other more general settings. Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 - a physical transmission medium. For example, in telecommunications, several telephone calls may be carried using one wire. Multiplexing originated in telegraphy in the 1870s, and is now widely applied in communications. In telephony, George Owen Squier is credited with the development of telephone carrier multiplexing in 1910. The multiplexed signal is transmitted over a communication channel such as a cable. The multiplexing divides the capacity of the communication channel into several logical channels, one for each message signal or data stream to be transferred. A reverse process, known as demultiplexing, extracts the original channels on the receiver end. A device that performs the multiplexing is called a multiplexer (MUX), and a dev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stereophonic Sound
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 of two loudspeakers (or stereo headphones) in such a way as to create the impression of sound heard from various directions, as in natural hearing. Because the multi-dimensional perspective is the crucial aspect, the term ''stereophonic'' also applies to systems with more than two channels or speakers such as quadraphonic and surround sound. Binaural recording, Binaural sound systems are also ''stereophonic''. Stereo sound has been in common use since the 1970s in entertainment media such as broadcast radio, recorded music, television, video cameras, cinema, computer audio, and internet. Etymology The word ''stereophonic'' derives from the Greek language, Greek (''stereós'', "firm, solid") + (''phōnḗ'', "sound, tone, voice") and i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 concatenation theory, also called string theory, string concatenation is a primitive notion. Syntax In many programming languages, string concatenation is a binary infix operator. The + (plus) operator is often overloaded to denote concatenation for string arguments: "Hello, " + "World" has the value "Hello, World". In other languages there is a separate operator, particularly to specify implicit type conversion to string, as opposed to more complicated behavior for generic plus. Examples include . in Edinburgh IMP, Perl, and PHP, .. in Lua, and & in Ada, AppleScript, and Visual Basic. Other syntax exists, like , , in PL/I and Oracle Database SQL. In a few languages, notably C, C++, and Python, there is string literal concatenation, mean ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate; that is, estimate the value of that function for an intermediate value of the independent variable. A closely related problem is the approximation of a complicated function by a simple function. Suppose the formula for some given function is known, but too complicated to evaluate efficiently. A few data points from the original function can be interpolated to produce a simpler function which is still fairly close to the original. The resulting gain in simplicity may outweigh the loss from interpolation error and give better performance in ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forward Error Correction
In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels. The central idea is the sender encodes the message with redundant information in the form of an ECC. The redundancy allows the receiver to detect a limited number of errors that may occur anywhere in the message, and often to correct these errors without retransmission. The American mathematician Richard Hamming pioneered this field in the 1940s and invented the first error-correcting code in 1950: the Hamming (7,4) code. ECC contrasts with error detection in that errors that are encountered can be corrected, not simply detected. The advantage is that a system using ECC does not require a reverse channel to request retransmission of data when an error occurs. The downside is that there is a fixed overhead that is added to the message, thereby requiring a h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 received symbols within the error burst. The integer parameter ''m'' is referred to as the ''guard band'' of the error burst. The last symbol in a burst and the first symbol in the following burst are accordingly separated by ''m'' correct symbols or more. The parameter ''m'' should be specified when describing an error burst. Channel model The Gilbert–Elliott model is a simple channel model introduced by Edgar Gilbert Edgar Nelson Gilbert (July 25, 1923 – June 15, 2013) was an American mathematician and coding theorist, a longtime researcher at Bell Laboratories whose accomplishments include the Gilbert–Varshamov bound in coding theory, the Gilbert–Ell ... and E. O. Elliott that is widely used for describing burst error patterns i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
