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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 4000 data bits in sequence (2.5 mm in length as seen on CD surface) and compensates for error bursts up to 12,000 bits (7.5 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 2024, this has not been implemented). Interleave Errors found in compact discs (CDs) are a c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compact Disc
The compact disc (CD) is a Digital media, digital optical disc data storage format co-developed by Philips and Sony to store and play digital audio recordings. It employs the Compact Disc Digital Audio (CD-DA) standard and was capable of holding of uncompressed stereo audio. First released in Japan in October 1982, the CD was the second optical disc format to reach the market, following the larger LaserDisc (LD). In later years, the technology was adapted for computer data storage as CD-ROM and subsequently expanded into various writable and multimedia formats. , over 200 billion CDs (including audio CDs, CD-ROMs, and CD-Rs) had been sold worldwide. Standard CDs have a diameter of and typically hold up to 74 minutes of audio or approximately of data. This was later regularly extended to 80 minutes or by reducing the spacing between data tracks, with some discs unofficially reaching up to 99 minutes or which falls outside established specifications. Smaller variants, such ... [...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 formalizations 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, and in some it is written without an operator. This is implemented in different ways: * Overloading the plus sign + Example from C#: "Hello, " + "World" has the value "Hello, World". * Dedicated operator, such as . in PHP, & in Visual Basic, and , , in SQL. This has the advantage over reusing + that it allows implicit type conversion to string. * string literal concatenation, which means that adjacent strings are concatenated without any operator. Example from C: "Hello, " "World" has the value "Hello, World". In many scientific publications or standards the conc ... [...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 functio ... [...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 se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parity (mathematics)
In mathematics, parity is the Property (mathematics), property of an integer of whether it is even or odd. An integer is even if it is divisible by 2, and odd if it is not.. For example, −4, 0, and 82 are even numbers, while −3, 5, 23, and 69 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers with decimals or fractions like 1/2 or 4.6978. 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; otherwise it is even—as ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stereophonic Sound
Stereophonic sound, commonly shortened to 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 the Internet. Etymology The word ''stereophonic'' derives from the Greek language, Greek (''stereós'', "firm, solid") + (''phōnḗ'', "sound, tone, voice" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forward Error Correction
In computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The central idea is that the sender encodes the message in a redundant way, most often by using an error correction code, or error correcting code (ECC). The redundancy allows the receiver not only to detect errors that may occur anywhere in the message, but often to correct a limited number of errors. Therefore a reverse channel to request re-transmission may not be needed. The cost is a fixed, higher forward channel bandwidth. 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. FEC can be applied in situations where re-transmissions are costly or impossible, such as one-way communication links or when transmitting to multiple receivers in m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Access Memory
Random-access memory (RAM; ) is a form of electronic 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 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 and magnetic tape), 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. In today's technology, random-access memory takes the form of integrated circuit (IC) chips with MOS (metal–oxide–semiconductor) memory cells. RAM is normally associated with volatile types of memory where stored information is lost if power is removed. The two main types of volatile random-access semiconductor memory are static ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error Correction
In information theory and coding theory with applications in computer science and telecommunications, 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 w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interpolation
In the mathematics, 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 (statistics), sampling or experimentation, which represent the values of a function for a limited number of values of the Dependent and independent variables, 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 function approximation, 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 gai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error Burst
In telecommunications, 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 and E. O. Elliott that is widely used for describing burst error patterns in transmission channels and enables simulations of the digital error performance of communications links. It is based on a Markov chain In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
