Overview

1
Overview

• All data can be corrupted, for reliable
  communications we must be able to detect and
  correct errors
• implemented at the data link and transport layers
  of the OSI model

2
Detection

• Redundancy - adding extra bits that indicate
  information about the data without repeating it
• types
• vertical
• longitudinal
• cyclical
• checksum

3
Error Detection

• Vertical Redundancy Check(VRC, or simply, Parity
  Check)
• Longitudinal Redundancy Check (LRC)
• Cyclic Redundancy Check (CRC)

4
Parity Check (Vertical Redundancy Check)

• Redundant bit is appended to each data unit
• Even parity the bit is set to 1 if number of 1s
  in the data is an odd number, thus making total
  number of 1s transmitted an even number
• Odd parity the bit is set to 1 if number of 1s
  in the data is an even number, thus making total
  number of 1s transmitted an odd number

5
Longitudinal

• Checks parity the same way as the vertical method
  but checks the data horizontally as well
• data is organized into columns and rows, each
  column is checked and given a parity bit, LRC is
  attached to the end of the data
• greatly increases the possibility of catching
  burst errors

6
Cyclical Redundancy Check(CRC)

• Common in data link protocols (CRC)
• data is binary divided (divisor is predetermined)
  remainder is appended to the data
• remainder is appended so that the data can be
  evenly divided by a second binary number
• remainder is 1 bit less than the divisor

7
Checksum

• Used in hardware and files
• at the sender, the data is divided into equal
  chunks of the same length
• the chunks are added together using ones
  compliments so that the total is the same length
  as a chunk
• the total is then complimented and the result is
  added to the data

8
Checksum cont

• The receiver chops the data up into the same size
  chunks and adds them using the ones compliment
• the total is summed with the checksum and if the
  result has a compliment that is all 0s then the
  data is assumed to be O.K.
• detects all odd and most even bit errors can
  still have errors

9
Hamming Code

• Redundancy bits do not have to come at the end of
  the data
• d d d r8 d d d r4 d r2 r1
• places a series of redundancy bits within the
  data, each r bit checks the parity on a different
  group of bits
• r1 1,3,5,7,9,11
• r2 2,3,6,7,10, 11
• r4 4,5,6,7
• r8 8,9,10,11

10
Hamming Code

• Receiver recalculates the VRC using the same bit
  sets and the parity (r) bits
• it assembles the parity values into a binary
  number in order of position
• r8, r4, r2, r1
• this binary number gives the position of the bit
  in error
• multiple bit errors require much more overhead