Error Detection and Correction

1. A significant role of the Data Link layer is to convert the potentially unreliable physical link between two machines into an apparently very reliable link.

2. This is done by including redundant information in each transmitted frame. Depending on the nature of the link and the data one can either:

   • include just enough redundancy to make it possible to detect errors and then arrange for the retransmission of damaged frames, or

   • include enough redundancy to enable the receiver to correct any errors produced during transmission.
   Most current networks take the former approach.

3. Codes for detecting (and even for correcting) errors are largely based on generalizing the simple notion of a parity bit.

   • Given a set of bits, a parity bit is an extra binary digit added to the group so that the total number of one's in the group is even (or odd if you prefer).

   • For example, a few "random" bytes of binary data are shown below with appropriate digits added as parity bits in a ninth column.

     0	1	0	1	0	1	0	1	0
     0	1	1	1	1	0	0	1	1
     0	0	0	0	0	0	0	0	1

4. Used in this simple way, parity bits are a rather weak mechanism for detecting errors.

   • A single parity bit can not detect any error in which an even number of bits are changed.

   • Errors in real communication lines tend to effect many consecutive bits rather than one isolated bit (these are called burst errors.

5. By associating several parity bits with a message so that each parity bit is determined by a different subset of the message bits and being clever about the placement of the parity bits one can do much better.

   • Simply adding two bits per byte with one bit for the odd positions and one for the evens enables one to recognize any error of up to three bits.

   • If one organized data into a table, adds a column of parity bits as above and then sends the data by columns from left to right, one can detect any error whose length is less than two columns.