Wireless networks - Lecture 5: Error detecting and correcting techniques

Wireless Networks

Lecture 5
Error Detecting and Correcting Techniques (Part II)
Dr. Ghalib A. Shah

1


Outlines
 Review of previous lecture #3
 Block Codes
► Hamming
► BCH
► Reed Solmon

 ARQ
► Sliding window
► Go-back-N

 Summary of today’s lecture
2


Last Lecture Review
 Transmission Errors
 Parity Check
► Single-bit parity
► 2D parity

 Cyclic Redundancy Check

 Block Error Code

3


Hamming Code
 Designed to correct single bit errors
 Family of (n, k) block error­correcting codes with 
parameters:
►
►
►
►

Block length:
n = 2m – 1
Number of data bits: k = 2m – m – 1
Number of check bits: n – k = m
Minimum distance: dmin = 3

 Single­error­correcting (SEC) code
► SEC double­error­detecting (SEC­DED) code

4


Example of Error Detection/Correction

C1
C2

1 1 0 1 1
0 0 0 0 1

XOR

1 1 0 1 0

Hamming distance =3
Received Codeword (Cr) =1 0 0 1 1
C1
Cr

1 1 0 1 1
1 0 0 1 1

XOR

0 1 0 0 0

C2
Cr

0 0 0 0 1
1 0 0 1 1

XOR

1 0 0 1 0

5


Hamming Code Process
 Encoding: k data bits + (n ­k) check bits
 Decoding: compares received (n ­k) bits with 
calculated (n ­k) bits using XOR
► Resulting (n ­k) bits called syndrome word
► Syndrome range is between 0 and 2(n­k)­1
► Each bit of syndrome indicates a match (0) or conflict (1) 
in that bit position

6


Example of Hamming Encode
 Data =00111001
Bit Position
Bit Position
Bit Position
Bit Position
Bit Position
Pos. Number
Pos. Number
Pos. Number
Pos. Number
Pos. Number
Trans. Block
Trans. Block
Trans. Block

Trans. Block
Trans. Block
Check bits

12
12
12
12 11
11
11 10
10
10 999
12
11
10

888

777

666

555

444

33

22

11

Position
1100 1011 1010
1001 1000Code
0111 0110 0101 0100 0011 0010 0001
1100
11001011
1011
10111010
1010
1010 1001
1001
1001 1000
1000
1000 0111
0111
0111 0110
0110
0110 0101
0101
0101 0100
0100
0011
0010
0001
1100
1100
1011
1010

1001
1000
0111
0110
0101
0100 0011
0011 0010
0010 0001
0001
1010
10

000

000

111

111
9
7

0x
x
0

11
11001000
0111

3

0011

XOR

0111

00
0

1x
x
1

7

11
1

1
X
x
1

1
X
X
1

Decoding Hamming

Bit Position
Pos. Number
Trans. Block
Trans. Block

12 11 10

9

8

7

6

5

4

3

2

1

1100 1011 Position
1010 1001 1000 0111Code

0110 0101 0100 0011 0010 0001
1010
10

0
0

0
0

1
1

1
1

9

0
0

1
1

0
1

0

0

1001

7

0111

6

0110

3

0011

XOR

0110

1
1

8

1
1

1
1

1

1


BCH Codes
 BCH  Discoverer: Bose, Chaudhuri and 
Hocquenghem.
 Multiple error correcting codes
 Generalization of Hamming Code.
 Flexibility in choice of parameters 
► Block length, code rate

9


BCH Codes
 For positive pair of integers m  and t, a (n, k)
BCH code has parameters:
► Block length: n =2m  – 1
► Number of check bits: n – k <= m t
► Minimum distance:d min >=2t +1

 Correct combinations of t or fewer errors
 The generator polynomial can be constructed
from the factors of (X2m-1 +1)

10


Reed­Solomon Codes
 Subclass of nonbinary BCH codes

 Data processed in chunks of m bits, called 
symbols
 An (n, k) RS code has parameters:
► Symbol length: m bits per symbol
► Block length: n = 2m – 1 symbols = m(2m – 1) bits
► Data length: k symbols
► Size of check code: n – k = 2t symbols = m(2t) 
bits
► Minimum distance: dmin = 2t + 1 symbols
11


Automatic Repeat Request
 Mechanism used in data link control and transport 
protocols
 Relies on use of an error detection code (such as 
CRC)
 Flow Control
 Error Control

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Flow Control
 Assures that transmitting entity does not overwhelm a 
receiving entity with data
 Protocols with flow control mechanism allow multiple PDUs 
in transit at the same time
 PDUs arrive in same order they’re sent
 Sliding­window flow control

► Transmitter maintains list (window) of sequence numbers allowed to 
send
► Receiver maintains list allowed to receive

13


Flow Control 
 Reasons for breaking up a block of data before 
transmitting:
► Limited buffer size of receiver
► Retransmission of PDU due to error requires smaller 
amounts of data to be retransmitted
► On shared medium, larger PDUs occupy medium for 
extended period, causing delays at other sending stations

14


Flow Control

15


Error Control
 Mechanisms to detect and correct transmission 
errors
 Types of errors:
► Lost PDU : a PDU fails to arrive
► Damaged PDU : PDU arrives with errors

16


Error Control Requirements
 Error detection
► Receiver detects errors and discards PDUs

 Positive acknowledgement
► Destination returns acknowledgment of  received, error­free PDUs

 Retransmission after timeout
► Source retransmits unacknowledged PDU

 Negative acknowledgement and retransmission
► Destination returns negative acknowledgment to PDUs in error

17


Go-Back-N
 Improve Stop-and-Wait by not waiting!
 Keep channel busy by continuing to send frames
 Allow a window of up to Ws outstanding frames
 Use m -bit sequence numbering
 If ACK for oldest frame arrives before window is
exhausted, we can continue transmitting
 If window is exhausted, pull back and retransmit all
outstanding frames
 Alternative: Use timeout

18


Go-Back-N ARQ
4 frames are outstanding; so go back 4

Go-Back-4:
A

fr
0

fr
1

fr
2

fr
3

fr
4

fr
5

fr
6

fr
3

fr
4

fr
5

fr
6

fr
7

fr
8

Time

fr
9

B
A
C
K
1

Rnext 0

1

A
C
K
2

2

A
C
K
3

3

out of sequence
frames

3

A
C
K
4

4

A
C
K
5

5

A
C
K
7

A
C
K
6

6

7

A
C
K
8

8

A
C

K
9

9

► Frame transmission are pipe line d to keep the channel busy
► Frame with errors and subsequent out-of-sequence frames are ignored
► Transmitter is forced to go back when window of 4 is exhausted
19


Window size long enough to cover round trip time

Stop-and-Wait ARQ
f0
A
B

Time-out expires

A
C
K
1

Receiver is
looking for
Rnext=0

Go-Back-N ARQ

Time

f1

f0

Four frames are outstanding; so go back 4

fr0 f1 f2

f3

f0 f1 f2 f3 f4 f5 f6

Time

A
B

Receiver is Out-oflooking for sequence
Rnext=0
frames

A
C
K
1

A

C
K
2

A
C
K
3

A
C
K
4

A
C
K
5

A
C
K
6

20


Go-Back-N with Timeout
 Problem with Go-Back-N as presented:
► If frame is lost and source does not have frame to

send, then window will not be exhausted and
recovery will not commence

 Use a timeout with each frame
► When timeout expires, resend all outstanding frames

21


Go-Back-N Transmitter & Receiver
Receiver

Transmitter
Send Window
...
Frames
transmitted S
last
and ACKed

Srecent
Buffers

Timer

Slast

Timer

Slast+1

Receive Window

Slast+Ws-1
oldest unACKed frame

...
Timer

Srecent

most recent
transmission

...
Slast+Ws-1

max Seq #
allowed

Frames
received

Rnext

Receiver will only accept
a frame that is error-free and
that has sequence number Rnext
When such frame arrives Rnext is
incremented by one, so the

receive window slides forward by
one
22


Go­back­N ARQ
 Acknowledgments
► RR = receive ready (no errors occur)
► REJ = reject (error detected)

 Contingencies
► Damaged PDU
► Damaged RR
► Damaged REJ

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