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

Detection

• Redundancy - adding extra bits that indicate information about the data without repeating it

• types– vertical– longitudinal– cyclical– checksum

Error Detection

• Vertical Redundancy Check(VRC, or simply, Parity Check)

• Longitudinal Redundancy Check (LRC)

• Cyclic Redundancy Check (CRC)

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

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

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

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 one’s 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

Checksum con’t

• The receiver chops the data up into the same size chunks and adds them using the one’s compliment

• the total is summed with the checksum and if the result has a compliment that is all 0’s then the data is assumed to be O.K.

• detects all odd and most even bit errors – can still have errors

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

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