Data Link Layer 1

2

Single-bit error 3

Multiple-bit error 4

Burst error 5

Error Control Detecting errors Correcting errors – Forward error correction – Automatic repeat request 6

Redundancy To detect or correct errors, redundant bits of data must be added 7

Common Detection Methods Parity check Cyclic Redundancy Check Checksum 8

Parity Check Most common, least complex Single bit is added to a block Two schemes: – Even parity – Maintain even number of 1s E.g., 1011  – Odd parity – Maintain odd number of 1s E.g., 1011 

Example: Parity Check 10 Suppose the sender wants to send the word world. In ASCII the five characters are coded (with even parity) as The following shows the actual bits sent Suppose the sender wants to send the word world. In ASCII the five characters are coded (with even parity) as The following shows the actual bits sent

Example: Parity Check 11 Receiver receives this sequence of words: Which blocks are accepted? Which are rejected?

Parity-Check: Encoding/Decoding 12

Performance of Parity Check Can 1-bit errors be detected? Can 2-bit errors be detected? 13

2D Parity Check 14 What is its performance?

2D Parity Check: Performance 15

2D Parity Check: Performance 16

Cyclic Redundancy Check In a cyclic code, rotating a codeword always results in another codeword 17

CRC Encoder/Decoder 18

CRC Generator 19

Checking CRC 20

Check sum 21

Check sum 22

Checksum 23

Checksum 24

Checksum 25

Checksum 26

Hamming code 27

Hamming code 28

Hamming code 29

Hamming code 30

Hamming code 31