Error Control

The bit stream transmitted by the physical layer is not certain to be error free. The data link layer is accountable for error detection and correction. The most general error control method is to calculate and append some form of a checksum to every outgoing frame at the sender end data link  layer and to recalculate the checksum and validate it  with the received checksum at the receiver end side. If both of them are equal, then the frame is correctly received else it is incorrect. The checksums may be of 2 types:

Error detecting: Receiver can only sense the error in the frame and can inform the sender about it.

Error detecting and correcting: The receiver can not only detect the error but also right it.

Examples of Error Detecting methods:

• Parity bit:

Plain example of error detection technique is parity bit. The parity bit is chosen that the number of one bits in the code word is either even ( for even parity) or odd (for odd parity). For instance when 10110101 is transmitted then for even parity an one will be appended to the data and for odd parity a zero will be appended. This scheme can detect only single bits. So if two or more bits are altered then that cannot be detected.

• Longitudinal Redundancy Checksum:

Longitudinal Redundancy Checksum is an error detecting method which overcomes the difficulty of two incorrect bits. In this concept of parity bit  is used but with somewhat more intelligence. With all byte we send one parity bit  then send one additional byte which have the parity equivalent to the each bit position of the sent bytes. So the parity bit can be set in both horizontal direction and vertical direction. If one bit get damaged we can tell which row and column have error then we locate the intersection of the two and determine the incorrect bit. If two bits are in error and they are in the dissimilar column and row then they can be detected. If the error are in the similar column then the row will distinguish and vice versa. Parity can sense the only odd number of errors. If they are even and spread in a fashion that in all direction then LRC may not be able to find out the error.

• Cyclic Redundancy Checksum (CRC):

Let we have an n-bit message. The sender adds a k-bit Frame Check Sequence (FCS) to this message before transfer. The resulting (n+k) bit message is divisible by some (k+1) bit number. The receiver divides the message ((n+k)-bit) by the same (k+1)-bit number and if there is no remainder and assumes that there was no error. How do we decide this number?

For example, if k=12 then 1000000000000 (thirteen bit number) can be chosen, but this is a pretty bad choice. Because it will result in a zero remainder for all (n+k) bit messages with the last twelve bits zero. Thus, any bits flipping beyond the last twelve go undetected. If the value of is k=12, and we take 1110001000110 as the thirteen bit number (by the way, in decimal representation this turns out to be 7238). This will be incapable of detecting error only  if  the  corrupt  message  and  original message  have  a  variation of a multiple of 7238. The probablilty of this is low, a lot lower than the probability that anything beyond  the  last  tweleve bits  flips.  In  practice,  this  number  is  chosen  after analyzing common network transmission errors and then selecting a number which is likely to notice these common errors.

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