Crc Error Probability
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a key word k that is known to both the transmitter and the receiver. The remainder r left after dividing M by k constitutes the "check word"
Cyclic Redundancy Check In Computer Networks
for the given message. The transmitter sends both the message string M and crc example the check word r, and the receiver can then check the data by repeating the calculation, dividing M by the key
Crc Calculator
word k, and verifying that the remainder is r. The only novel aspect of the CRC process is that it uses a simplified form of arithmetic, which we'll explain below, in order to cyclic redundancy check ppt perform the division. By the way, this method of checking for errors is obviously not foolproof, because there are many different message strings that give a remainder of r when divided by k. In fact, about 1 out of every k randomly selected strings will give any specific remainder. Thus, if our message string is garbled in transmission, there is a chance (about 1/k, assuming the corrupted message crc calculation is random) that the garbled version would agree with the check word. In such a case the error would go undetected. Nevertheless, by making k large enough, the chances of a random error going undetected can be made extremely small. That's really all there is to it. The rest of this discussion will consist simply of refining this basic idea to optimize its effectiveness, describing the simplified arithmetic that is used to streamline the computations for maximum efficiency when processing binary strings. When discussing CRCs it's customary to present the key word k in the form of a "generator polynomial" whose coefficients are the binary bits of the number k. For example, suppose we want our CRC to use the key k=37. This number written in binary is 100101, and expressed as a polynomial it is x^5 + x^2 + 1. In order to implement a CRC based on this polynomial, the transmitter and receiver must have agreed in advance that this is the key word they intend to use. So, for the sake of discussion, let's say we have agreed to use the generator polynomial 100101. By the way, it's worth noting that the remainder of any word divided by
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Cyclic Redundancy Check Error
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