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Parvaresh–Vardy Code
Parvaresh–Vardy codes are a family of error-correcting codes first described in 2005 by Farzad Parvaresh and Alexander Vardy. They can be used for efficient list-decoding In coding theory, list decoding is an alternative to unique decoding of error-correcting codes for large error rates. The notion was proposed by Elias in the 1950s. The main idea behind list decoding is that the decoding algorithm instead of out .... See also * Reed–Solomon code * Folded Reed–Solomon code References Error detection and correction Coding theory {{comp-sci-theory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error-correcting Code
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] |
Alexander Vardy
Alexander Vardy (, ; 12 November 1963 - 11 March 2022) was a Russian-born and Israeli-educated electrical engineer known for his expertise in coding theory.. He held the Jack Keil Wolf Endowed Chair in Electrical Engineering at the University of California, San Diego.. The Parvaresh–Vardy codes are named after him. Vardy was born in Moscow in 1963.. He graduated from the Technion – Israel Institute of Technology in 1985, and completed his Ph.D. in 1991 at Tel Aviv University. During his graduate studies, he also worked on electronic countermeasures for the Israeli Air Force, attaining the rank of Israel Defense Forces ranks, Seren (Captain). He became a researcher at the IBM Almaden Research Center for two years, then became a faculty member of the University of Illinois at Urbana–Champaign before moving to University of California, San Diego, UCSD in 1996. He served as editor-in-chief of the ''IEEE Transactions on Information Theory'' from 1998 to 2001. In 2004 a paper by Ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List-decoding
In coding theory, list decoding is an alternative to unique decoding of error-correcting codes for large error rates. The notion was proposed by Elias in the 1950s. The main idea behind list decoding is that the decoding algorithm instead of outputting a single possible message outputs a list of possibilities one of which is correct. This allows for handling a greater number of errors than that allowed by unique decoding. The unique decoding model in coding theory, which is constrained to output a single valid codeword from the received word could not tolerate a greater fraction of errors. This resulted in a gap between the error-correction performance for stochastic noise models (proposed by Shannon) and the adversarial noise model (considered by Richard Hamming). Since the mid 90s, significant algorithmic progress by the coding theory community has bridged this gap. Much of this progress is based on a relaxed error-correction model called list decoding, wherein the decoder ou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Folded Reed–Solomon Code
In coding theory, folded Reed–Solomon codes are like Reed–Solomon codes, which are obtained by mapping m Reed–Solomon codewords over a larger alphabet by careful bundling of codeword symbols. Folded Reed–Solomon codes are also a special case of Parvaresh–Vardy codes. Using optimal parameters one can decode with a code rate, rate of ''R'', and achieve a decoding radius of 1 − ''R''. The term "folded Reed–Solomon codes" was coined in a paper by V.Y. Krachkovsky with an algorithm that presented Reed–Solomon codes with many random "phased burst" errors. The list-decoding algorithm for folded RS codes corrects beyond the 1-\sqrt bound for Reed–Solomon codes achieved by the Venkatesan Guruswami, Guruswami–Madhu Sudan, Sudan algorithm for such phased burst errors. History One of the ongoing challenges in Coding Theory is to have error correcting codes achieve an optimal trade-off between (Coding) Rate and Error-Correction Radius. Though this may no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error Detection And 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] |
