Error Detecting methods

The most popular error detecting methods are:

Parity check method.
Cyclic Redundancy check method (CRC)

Parity Check Method

Errors may occur in recording data on magnetic media due to bad tracks, sectors on the recording surface. Errors may also be caused by electrical disturbances during data transmission between two distant computers. It is thus necessary to device methods to guard against such errors. The main principle used for this purpose in coded data is the introduction of extra bits in the code to aid error detection.

A common method is the use of parity check bit along with each character code to be transmitted. As a simple example of an error-detecting code, consider a code in which a single parity bit is appended to the data. The parity bit is chosen so that the number of 1 bits in the codeword or character code to be transmitted or recorded is even or odd.

For example, when 10110101 is sent in even parity by adding a bit at the end, it becomes 101101011, where as 10110001 becomes 101100010 with even parity. A code with a single parity but has a distance 2, since any single-bit error produces a code word with the wrong parity, It Can be used to detect single errors. Two errors cannot be detected by this scheme as the total number of 1s in the code will remain even after two bits change. As the probability of more than one error occurring is in practice very small this scheme is commonly accepted as sufficient.

Instead of appending a parity check but which makes the total number of 1s in the code even, one may choose to append a parity check bit which makes the number of 1s in the odd. Such a parity check is known as an odd parity bit. This scheme also facilities detection of a single error in a code.

Cyclic Redundancy check method (CRC)

Another popular method is in wide spread for error detection. It is the polynomial code also known as cyclic redundancy code or CRC code. C.R.C codes are based upon treating bit steam as a representations of polynomials with co-efficient of zero and one only.

A k +bit frame is regarded as the co-efficient list for a polynomial with k terms, ranging from xk-1 to x0 . Such a polynomial is said to be of degrees k-1 the high order (left most) bit is the coefficient of xk-1 , the next bit the coefficient of x k-2 , and so on. For eg : 110001 has six bits and thus represents a six-term polynomial with coefficient 1,1,0,0,0 and 1 : x5+x4+x+0

When the polynomial code method is employed, the sender and receiver must agreed upon a generator polynomial, G(x), in advance. Both the high-and-low-order bits of the generator must be 1. To compute the checksum for some frame with m bits, corresponding to the polynomial M(x), the frame must be longer than the generator polynomial.

The idea is to append a checksum to the end of the frame in such a way that polynomial represent by the checksummed frame, it tries dividing it by G(x). If there is a remainder, there has been a transmission error!

Three polynomials have become international standards:

CRC – 12 = x12+x11+x3+x2+x1+1
CRC – 16 = x16+x15+x2+1
CRC- CCITT = x16+x12+x5+1

All three contains x+1 as a prime factor CRC-12 is used when character length is 6 bits. The other two are used for 3-bits character. A 16-bit checksum, such as CRC- 16 or CRC – CCITT, catches all single and double errors, all errors with an odd number of bits, all burst errors of length 16 or less, 99.997 percent of 17 bit error bursts and 99.998 percent 18 bits longer bursts.

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