40 Communication Networks
Copyright © 2005 PragSoft
to retransmit frames because the receiver has been slow in acknowledging their receipt. When piggybacking is used, the receiver will send a separate
acknowledgment frame if T2 expires.
3.2.3. Error Checking
No physical medium can guarantee error-free transmission of data. Errors occur because of interference from the environment surrounding the transmission medium
or because of artifacts introduced by the equipment or the medium itself. In case of copper wires, for example, thermal noise, electrical noise, and impulse noise are
some of the most common causes.
The most important role of the data link layer is to provide error-free transmission. To do this, it uses an error checking scheme to detect errors, and
overcomes them by retransmitting corrupted frames. Many different error detection methods have been devised. We will discuss two popular methods in this section:
parity checking and cyclic redundancy code.
Parity checking
is a simple error detection method used with character- oriented protocols. One bit in every character bit sequence is reserved for parity.
This bit is set by the transmitter to 0 or 1 so that the total number of 1 bits in the character is always even in case of even parity checking or always odd in case of
odd parity checking. The receiver checks the parity bit of each character to see if it is as expected. Figure 3.29 illustrates the method for an even parity checking
scheme.
Figure 3.29 Even parity error checking.
1 1
1 1
1 1
1 1
parity bit
character bit sequence
Parity checking is effective in detecting an odd number of bit errors in a character single bit errors represent the most common case. If an even number of bits in a
character are corrupted then this will go unnoticed, because the parity bit will seem correct.
Cyclic Redundancy Check CRC is a more sophisticated method used with
bit-oriented protocols. It is also called the polynomial code — so named because it treats the single bits in a bit sequence as the coefficients of an imaginary polynomial.
For example, the bit sequence 101001 represents the polynomial:
1
x
5 + 0
x
4 + 1
x
3 + 0
x
2 + 0
x
1 + 1
x
www.pragsoft.com Chapter 3: The Data Link Layer
41
= x
5 +
x
3 +
x This polynomial is said to be of order 5, because its highest-order term is x
5
.
CRC relies on the use of a generator polynomial, the choice of which is fairly
arbitrary, except that the high and low order bits of its bit sequence must be 1 e.g., 10111 is acceptable, but 0101 and 10110 are not and that the transmitter and the
receiver must use exactly the same generator polynomial.
CRC works as follows. Given a message bit sequence m represented by the polynomial mx, and a generator polynomial gx of order k, m is appended with
exactly k zero bits. The result is equivalent to the polynomial px = x
k
mx. px is divided by gx and the remainder is added to px to produce the final polynomial
qx:
qx = px + px rem gx
It follows that qx is divisible by gx. The transmitter calculates q using m and g and then transmits q instead of m. If any of the bits in q are changed due to
transmission errors, qx has a very high probability of no longer being divisible by gx. This is checked by the receiver to detect transmission errors. If there are no
errors, the receiver extracts m from q by discarding the k low-order bits and this will be identical to the original message.
The polynomial calculation procedures described above serve only as a conceptual model. In practice, equivalent binary operations are used instead. The
binary operations are surprisingly simple, to the point that the whole process is usually implemented in hardware. Calculating q involves the following steps:
1. Given a bit sequence m and a generator polynomial bit sequence g of order k, append m with exactly k zero bits to produce bit sequence p. For example:
m = 100101110101 g = 10111
k = 4 p
= 1001011101010000 2. Divide p by g, using modulo 2 arithmetic, to produce a remainder r. Modulo 2
arithmetic operations are similar to binary operations, except that there are no borrows or carries. Addition and subtraction in modulo 2 are identical to the
binary exclusive or operation. Continuing with our example:
11001000110 quotient
100101 1101011110010000
100101 0100001
100101 000100110
100101 0000110100
42 Communication Networks
Copyright © 2005 PragSoft
100101 0100010
100101 1110
remainder
r = 1110
3. Add r to p to produce q: q
= 1001011101010000 + 1110 = 1001011101011110
The effectiveness of CRC depends to a large extent on the choice of the generator polynomial. In practice, polynomials of order 16 are widely used. Hence
16 bits two octets
3
are needed for storing the remainder, which appears as the checksum field in the frame see Figure 3.1. Such polynomials are more than 99
effective in catching a variety of errors.
3.2.4. Retransmission
