An Algorithm For Error Correcting Cyclic Redundancy Checks
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DevJolt Awards Channels▼ CloudMobileParallel.NETJVM LanguagesC/C++ToolsDesignTestingWeb DevJolt Awards Tweet Permalink An Algorithm for Error Correcting Cyclic Redundance Checks By Bill McDaniel, June 01, 2003 A straightforward technique to leverage the error-correcting capability inherent in CRCs. An Algorithm for Error Correcting Cyclic Redundance Checks
Crc Error Detection
Programmers have used the Cyclic Redundance Check (CRC) algorithm for years to uncover cyclic redundancy check example errors in a data transmission. It turns out that you can also use CRCs to correct a single-bit error in
Cyclic Redundancy Check In Computer Networks
any transmission. I first heard about error correcting CRCs in a conversation I had several years ago [1]. At the time, I thought this feature of CRCs was general knowledge, but as crc algorithm I did more research, I saw no mention of CRC error correction in the popular literature. The traditional response to a CRC error is re-transmission. However, the advance of computer technology has led to some situations where it is actually preferable to correct single-bit errors rather than to resend. Some examples include: Satellite transmission -- If a host is sending data via a satellite, crc check the cost of sending a regular packet is high, so the cost of a resend just doubles the price for the packet. High-speed transmission -- In the future, there may be a tendency to push the technology. (Let's crank this baby up and see what it will do.)The faster bits move through a medium, the higher the probability of error. PowerLine Carriers -- Metricom Corporation, a supplier of integrated circuits for computer applications states, "There is a growing interest in the use of PowerLine Carrier (PLC) for data communication using the intrabuilding electric power distribution circuits. Power lines were not designed for data communications and exhibit highly variable levels of impedance, signal attenuation and noise... Harmful effects of impulse noise on data communications systems can be expected." [2]. You could also use CRC error correction for storage devices -- both hard disk and RAM -- and for compression programs. The way compression programs are written now, it is often difficult to recover the original data if one bit is lost. Bit errors typically occur in bursts. Tannenbaum describes a method for recovering from burst errors that lends itself to a 1-bit error
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Cyclic Redundancy Check Ppt
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reliable link. This is done by including redundant information in each transmitted frame. Depending on the nature of the link and the data one can either: http://www.cs.jhu.edu/~scheideler/courses/600.344_S02/CRC.html include just enough redundancy to make it possible to detect errors and then arrange for the retransmission of damaged frames, or include enough redundancy to enable the receiver to correct any errors produced during transmission. Most current networks take the former approach. One widely used parity bit based error detection scheme is the cyclic redundancy check or CRC. The CRC is cyclic redundancy based on some fairly impressive looking mathematics. It is helpful as you deal with its mathematical description that you recall that it is ultimately just a way to use parity bits. The presentation of the CRC is based on two simple but not quite "everyday" bits of mathematics: polynomial division arithmetic over the field of integers mod 2. Arithmetic over the cyclic redundancy check field of integers mod 2 is simply arithmetic on single bit binary numbers with all carries (overflows) ignored. So 1 + 1 = 0 and so does 1 - 1. In fact, addition and subtraction are equivalent in this form of arithmetic. Polynomial division isn't too bad either. There is an algorithm for performing polynomial division that looks a lot like the standard algorithm for integer division. More interestingly from the point of view of understanding the CRC, the definition of division (i.e. the definition of the quotient and remainder) are parallel. When one says "dividing a by b produces quotient q with remainder r" where all the quantities involved are positive integers one really means that a = q b + r and that 0 <=r < b When one says "dividing a by b produces quotient q with remainder r" where all the quantities are polynomials, one really means the same thing as when working with integers except that the meaning of "less than" is a bit different. For polynomials, less than means of lesser degree. So, the remain
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