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Cyclic Redundancy Check Code

Cyclic redundancy check (CRC) codes provide a reasonably high level of protection at low redundancy level. The cycle code for a given data word is generated as follows. The data word is first appended by a number of 0s equal to the number of check bits to be added. This new data bit sequence is then divided by a special binary word whose length equals n + 1, n being the number of check bits to be added. The remainder obtained as a result of modulo-2 division is then added to the dividend bitsequence to get the cyclic code. The code word so generated is completely divisible by the divisor used in the generation of the code. Thus, when the received code word is again divided by the same divisor, an error-free reception should lead to an all ‘0’ remainder. A nonzero remainder is indicative of the presence of errors.

The probability of error detection depends upon the number of check bits, n, used to construct the cyclic code. It is 100 % for single-bit and two-bit errors. It is also 100 % when an odd number of bits are in error and the error bursts have a length less than n + 1. The probability of detection reduces to 1 – (1/2)n−1 for an error burst length equal to n + 1, and to 1 – (1/2)n for an error burst length greater than n + 1.

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