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 • Evenparity: 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 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

8. 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

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