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Unformatted text preview: Computer Networks Error detection Saad Mneimneh Computer Science Hunter College of CUNY New York par i ty: the quality or state of being equal or equivalent 1 Introduction The existence of an error in the frame cannot be detected by analyzing the frame itself (why?). Therefore, extra bits must be used. These bits are added by the DLC as a trailer (see Figure 1), often known as a parity . The parity is a function of the data in the frame, and by checking the received parity against the received frame, the receiving DLC is able to detect whether certain types of errors have occurred. All framing techniques are sensitive to errors. For example, if an error occurs in DLE ETX, the receiver will not detect the end of the frame. A similar problem is that errors can cause the appearance of DLE ETX in the data itself; the receiver would interpret this as the end of the frame. In both cases, the perceived parity is essentially a random bit string in relation to the perceived frame, and the receiver fails to detect the error with a probability of 2- L , where L is the length of the parity. The same problem occurs in bit oriented framing with the flag disappearing or appearing due to errors. This problem is often called the data sensitivity problem of the DLC, since even though the parity is capable of detecting errors, a single error that creates or destroys a flag, plus a special combination of data bits to satisfy the perceived parity, causes an undetectable error. Similarly, an error in the length field causes the frame to be determined at the wrong point, and the receiver to look for the parity in the wrong place. The probability of such an error is smaller using a length field than using a flag (since errors can create false flags); however, an error in the length field makes it hard for the receiver to know where to look for subsequent frames. Re-synchronization after every frame is required for recovery in order to read the frames correctly, but this makes the length field redundant. Parity check is used by the receiving DLC to determine if a frame contains errors. If a frame is found to contain errors, the receiver requires the sender to retransmit the frame (thats mainly how error correction is performed). The following sections describe different parity check mechanisms. 1 2 Parity check codes 2.1 Single parity check A one bit parity is added to the frame. The parity bit is 1 if the frame contains an odd number of ones, and 0 otherwise. Here are two examples showing the added parity bit in a box. 1001010 1 0111010 After adding the parity bit, a frame contains an even number of ones. Therefore, the receiver counts the number of ones. If the number of ones is odd, an error must have occurred. If the number of ones is even, the receiver interprets this as no error, because an even number of errors cannot be detected. Therefore, the probability of not detecting errors is: Pr ( undetected error ) = X i> k 2 i p 2 i (1- p ) k- 2 i assuming independent errors (simplification), where...
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This note was uploaded on 03/27/2010 for the course CSCI 415 taught by Professor Saadmneimneh during the Spring '08 term at CUNY Hunter.
- Spring '08
- Computer Networks