Transcript Lektion 1-Introduktion

Multimedie- och
kommunikationssystem, lektion 6
Kap 6: Fort. digital transmission. Felhantering.
Note:
In a single-bit error, only one bit in the
data unit has changed.
10.1
Single-bit error
Note:
A burst error means that 2 or more bits
in the data unit have changed.
10.2
Burst error of length 5
Note:
Error detection uses the concept of
redundancy, which means adding
extra bits for detecting errors at the
destination.
10.3
Redundancy
10.4
Detection methods
Note:
In parity check, a parity bit is added to
every data unit so that the total
number of 1s is even
(or odd for odd-parity).
Example 1
Suppose the sender wants to send the word world. In ASCII (7-bit
code) the five characters are coded as
1110111 1101111 1110010 1101100 1100100
Even parity is used. The following shows the actual bits sent:
11101110 11011110 11100100 11011000 11001001
Example 3
Now suppose the word world in Example 1 is received by the
receiver without being corrupted in transmission.
11101110 11011110 11100100 11011000 11001001
The receiver counts the 1s in each character and comes up with
even numbers (6, 6, 4, 4, 4). The data are accepted.
Now suppose the word world in Example 1 is corrupted during
transmission.
11111110 11011110 11101100 11011000 11001001
The receiver counts the 1s in each character and comes up with
even and odd numbers (7, 6, 5, 4, 4). The receiver knows that the
data are corrupted, discards them, and asks for retransmission.
Note:
Simple parity check can detect all
single-bit errors. It can detect burst
errors only if the total number of
errors in each data unit is odd.
Note:
In two-dimensional parity check, a
block of bits is divided into rows and a
redundant row of bits is added to the
whole block.
10.6
Two-dimensional parity
Example 4
Suppose the following block is sent:
10101001 00111001 11011101 11100111 10101010
However, it is hit by a burst noise of length 8, and some bits are
corrupted.
10100000 00001001 11011101 11100111 10101010
When the receiver checks the parity bits, some of the bits do not
follow the even-parity rule and the whole block is discarded.
10100000 00001001 11011101 11100111 10101010
10.7
CRC generator and checker
CRC = Cyclic Redundency Check
”Vanlig” division
(Kvot)
03
5
(Nämnare)
17
17
Nominator (Täljare)
.15
2
Reminder (Rest)
Haltande liknelse med CRC: Om vi subtraherar täljaren (17)
med resten (2) vi ett tal som är jämnt delbart med nämnaren
(5). Om mottagaren tar emot något som inte är delbart med 5
har sannolikt att bitfel uppstått.
Modulo 2 Arithmetic
 In modulo 2 arithmetic addition and substruction are identical to
EXCLUSUVE OR (XOR) operation.
 Multiplication and division are the same as in base-2 arithmetic without
carries in addition or borrows in substraction.
0 XOR 0 = 0
0 XOR 1 = 1
1 XOR 0 = 1
1 XOR 1 = 0
Examples:
1011 XOR 0101 = 1110
1001 XOR 1101 = 0100
10.8
Binary division in a CRC generator
The number of 0s is
one less than the
number of bits in G
(divisor)
10.8
Binary division in a CRC generator
The first bit in the
numerator is 1. Then the
first bit in the quotient is 1.
The first bit in the quotient
is 1 and one times the
divisor results in this
Obtained by
XOR-ing 1001
and 1101
10.8
Binary division in a CRC generator
Transmitted data: 1 0 0 1 0 0 0 0 1
10.9
Binary division in CRC checker
Another Example
The transmitted data is
11010110111110
10.11
A polynomial representing a divisor
7th order
polynomial
8 bit divisor
Polynomyal representation
Based upon discrete mathetematics, where bit strings
are treated as polynomials.
k bit divisor is represented as (k-1) degree
polynomial with coefficients 0 and 1.
Example: 1010110 has 7 bits
It can be represented as a polynomial of 6th degree
1·x6 + 0·x5 + 1·x4 +0·x3 + 1·x2 + 1·x1 + 0·x0 =
x6 + x4 + x2 + x
Table 10.1 Standard polynomials
Name
Polynomial
Application
CRC-8
x8 + x 2 + x + 1
ATM header
CRC-10
x10 + x9 + x5 + x4 + x 2 + 1
ATM AAL
ITU-16
x16 + x12 + x5 + 1
HDLC
ITU-32
x32 + x26 + x23 + x22 + x16 + x12 + x11 + x10 + x8 + x7 +
x5 + x4 + x2 + x + 1
LANs
Example 5
It is obvious that we cannot choose x (binary 10), x2
(binary 100), etc, because then the reminder is 0. We cannot
chose a polynomial that is divisible by x, for example x2 +
x (binary 110). However, we can choose x + 1 (binary 11)
because it is not divisible by x, but is divisible by x + 1.
We can also choose x2 + 1 (binary 101) because it is
divisible by x + 1 (binary division).
How CRC Operates
 The sender wants to send k bits message
 The sender and the receiver must agree in advance on n+1
bit string called generator polynomial (divisor), G.
 G can be represented as n-degree polynomial
 n redundant bits are added to the k bits message. They are
called CRC bits.
k bits
Data bits to be sent
n bits
CRC bits
How CRC Operates (Cont.)
 The redundant bits are chosen in such a way that the
resulting k+n bit string is exactly divisible (with a
reminder=0) by G using modulo 2 arithmetic.
 The receiver divides the received data together with the
CRC bits by G using modulo 2 arithmetic.
 If the reminder is 0, then the string is considered to be without
errors
 If the reminder is not 0, the data unit is with errors and it is rejected
Example 6
The CRC-12
x12 + x11 + x3 + x + 1
which has a degree of 12, will detect all burst errors
affecting an odd number of bits, will detect all burst
errors with a length less than or equal to 12, and will
detect, 99.97 percent of the time, burst errors with a
length of 12 or more.
Example 6.7: CRC
Note:
The sender follows these steps:
•The unit is divided into k sections, each of n bits.
•All sections are added using one’s complement to get the sum.
•The sum is complemented and becomes the checksum.
•The checksum is sent with the data.
Column:
Carry from column 5
Example
7 6
5
3
2
1
1 0
Carry from column 4
1
Carry from column 3
 n=5 bit checksum.
 20 bit data gives
k=20/n=4 sections
(rows).
 The addition starts in
the last column.
 The bits are carried in
the columns before.
 The 6th and 7th bit are
added
 The sum is
complemented
4
1
1
Carry from column 2
1
Carry from column 1
1 0
Sum
Checksum
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
1
1
0
Example 7
Suppose the following block of 16 bits is to be sent using a
checksum of 8 bits.
10101001 00111001
The numbers are added using one’s complement
10101001
Sum
00111001
-----------11100010
Checksum
00011101
The pattern sent is
10101001 00111001 00011101
Note:
The receiver follows these steps:
•The unit is divided into k sections, each of n bits.
•All sections are added using one’s complement to get the sum.
•The sum is complemented.
•If the result is zero, the data are accepted: otherwise, rejected.
Example 8
Now suppose the receiver receives the pattern sent in Example 7
and there is no error.
10101001 00111001 00011101
When the receiver adds the three sections, it will get all 1s, which,
after complementing, is all 0s and shows that there is no error.
10101001
00111001
00011101
Sum
11111111
Complement
00000000 means that the pattern is OK.
Example 9
Now suppose there is a burst error of length 5 that affects 4 bits.
10101111 11111001 00011101
When the receiver adds the three sections, it gets
10101111
11111001
00011101
Partial Sum
1 11000101
Carry
Sum
Complement
1
11000110
00111001
the pattern is corrupted.
11.1 Flow and Error Control
Flow Control (Flödesstyrning)
Error Control (Felhantering)
•
•
Båda dessa funktioner hanteras av vissa
datalänkprotokoll (lager 2), i LLC-sublagret, t.ex.
vid trådlös kommunikation eller vid modem.
End-to-end flödesstyrning och felkontroll
hanteras av transportprotokollet TCP (lager 4).
Flow control
Necessary when data is being sent faster than it can be
processed by receiver to avoid that the receiver’s buffer is
overwhelmed.
Felhantering med hjälp av felrättande koder
FEC = Forward Error Correction.
Baseras på felrättande istället för felupptäckande koder.
Kräver ingen backkanal.
Två typer:
1. Faltningskoder (convolutional codes).
Ex:Vid Faltningskod med kodtakt (code rate) 1/3 infogas två redundanta bitar
mellan varje bit i nyttomeddelandet. Dessa felrättande bitar beräknas
kontinuerligt för varje inkommande bit i nyttomeddelandet.
2.
Blockkoder (block codes)
Ex: I digital-TV-systemet används en s.k. Read Salomon-kod med
beteckningen RS(204, 188, 8). Det innebär att nyttoinformationen delas
upp i 188 byte stora block. För varje block beräknas en felrättande kod,
som läggs till blocket så att blocket blir 204 byte. Redundanden är alltså
204 – 188 = 16 byte. Koden klarar 8 felaktiga byte.
Felhantering med hjälp av felupptäckande
koder
Alternativ 1: Bortkastning av felaktiga paket.
Alternativ 2: ARQ = Automatic Repeat reQuest
= automatisk omsändning av paket vid bitfel, eller om paketet
inte når fram.
I fortsättning kommer vi med begreppet ”error control”
eller ”felkontroll” att avse ARQ.
Protocols to be presented
 Idle RQ = Stop-and-wait ARQ
 Sliding Window Flow Control
 Go-back-N ARQ
 Selective Repeat ARQ
Sliding Window
Protocols
The Idle RQ (Repeat Request) Protocol
The simplest protocol for error and flow control
How the protocol operates:
 Source may not send a new frame until the receiver acknowledges
previous one.
 The receiver sends only positive acknowledgements (ACK) to notify
the sender that the frame was received.
 If the frame 0 was received, the ACK 1 is sent. In that way the sender
is notified that the receiver is expecting frame 1.
 The ID of the frame is called a sequence number.
 1 bit sequence numbers is sufficient. Sequence: 0 1 0 1 0 ... .
Figure 6.23 Idle RQ error control scheme: (a)
error free;
(b) corrupted I-frame;
Figure 6.24 Idle RQ link utilization.
(c) corrupted ACK-frame.
11.1
Normal operation
ACK n = Acknowledgement. Expecting frame number n
11.2
Stop-and-Wait ARQ, lost frame
Lost or Damaged Frame
 The sender starts a timer when it sends each frame
 If the ACK is not received before the timer expires, the
sender resends the same frame again
11.3
Stop-and-Wait ARQ, lost ACK frame
Lost or damaged ACK
 Lost ACK causes duplicate frames
 A duplicate frame is recognized by the sequence number
and is discarded
 The receiver sends the same ACK again
11.4
Stop-and-Wait ARQ, delayed ACK
Note:
Numbered acknowledgments are
needed if an acknowledgment is
delayed and the next frame is lost.
Piggybacking
 Usually the communication is in both ways – this means that
the sender is a receiver and the receiver is the sender, too.
(both send and receive data)
 To save on the processing and bandwidth the short ACKs
messages are not sent as separate frames. Instead, they may be
included in the frames with data.
 This technique is called piggybacking
Example 6.8: Idle RQ
Figure 6.25 Effect
of propagation
delay as a
function of data
transmission
rate; parts
correspond to
Example 6.8.
Example 6.9
11.5
Piggybacking
Efficiency of Stop-and-Wait
 Very inefficient, having in mind that most of the time the sender is idle
 Example: 40 km copper cable, 10 Mbps rate, 1000 bit frame,
 Signal in copper propagates at 2 x 108 m/sec
 Transmission time is 1000/10000000 (Takes 0.1 msec to transmit frame)
 Propagation time is 40000/ 2 x 108 (0.2 msec delay to begin arriving at the
receiver)
 Total time is 0.3 msec. to get to the receiver
 ACK transmission time is approximately 0 (assuming the ACK is very short
(length  0)
 0.2 msec is the time for the ACK to arrive at the sender
 Total time is 0.5 msec before the sender can transmit again
 0.5 ms for 0.1 msec frame or efficiency is 20%
Sliding-Window flow control
 Several frames can be sent without acknowledgement being received
 N is the window size – the maximum number of frames that can be sent
and not being acknowledged.
 The receiver must be able to buffer N frames.
 Sequence numbers are used to identify each frame. They are carried in the
header.
 The number of different sequence numbers must be at least N+1.
 If the field for sequence numbers allows m bits, the number of different
sequence number is 2m and the sequence numbers range from 0 to 2m-1.
In that case the maximum window size is N = 2m-1.
11.6 Sender sliding window
The sender window is the the set of frames that may be
transmitted before an ACK. It slides when the sender
has received an ACK and sent next frame.
11.7
Receiver sliding window
The receiver window is the the set of frames that may
be accepted before the buffer is full. While the buffer
is full, the receiver sends no ACK. The window of a
stuffed receiver slides when the receiver has
”consumed” a frame and thus sent an ACK.
Stop-and-Wait vs. Sliding Window
Window size N=3.
Sender
Sender
Receiver
Transmission +
propagation
Transmiss
time for the
ion time
packet
for the
packet
Transmission +
propagation
time for the
ACK
.
.
.
Sequence numbers are 1
bit long (0 or 1)
Frame
consumption
delay
Receiver
propagation
time
..
.
Frame
consumption
delay
...
Sequence numbers from 0 to 2m1. m-bit field for the seq. num.
Sender and Receiver Prospective
The window size
is 7
Sliding Window Flow Control
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
0
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
0
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
0
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
0
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
0
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
0
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
0
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
0
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
0
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
0
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
0
F0
F1
ACK1
F2
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
0
ACK2
F3
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
0
ACK3
F4
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
0
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
0
0
1
2
3
4
5
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7
0
1
2
3
4
5
6
7
0
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
0
ACK4
F5
ACK5
ACK6
N=6
ARQ with Sliding Window
Problems arise when some of the frames are discarded (errors or lost
frames). Two strategies are developed to deal with this problem:
 Go-back-N strategy
 The reciever simply discards all frames after the damaged frame without
sending acknowledgement.
 Selective repeat strategy
 The receiver keeps all the frames after the damaged frame. It sends negative
acknowledgement (NACK) for the damaged frame. When the sender finaly
notice that something is wrong it retransmits the bad frame.
The two strategies are trade-offs between bandwidth and data-link buffer
space.
Go-Back-N Strategy
 If a frame is lost, the lost frame and all the frames sent after it are
sent again.
 Sending window of size N, receiving window of size 1.
 The sender has to buffer N frames
 Bandwidth is wasted.
11.9
Go-Back-N ARQ, normal operation
11.10
Go-Back-N ARQ, lost frame
11.11 Go-Back-N ARQ: sender window size
Selective Repeat Strategy
 Only retransmit the frames that are in error
 Both sending and receiving window are of size N
11.13
Selective Repeat ARQ, lost frame
11.14
Selective Repeat ARQ, sender window size
Bandwidth – Delay Product
 The product of the bit rate (bandwidth expressed as bits per
seconds) and the propagation time gives the number of bits
that can be on the channel and thus can give orientation
about the window size
 When propagation time is high (for example in satellite
channels), the window size need to be larger
Example 1
In a Stop-and-Wait ARQ system, the bandwidth of the line is 1 Mbps, and 1 bit
takes 20 ms to make a round trip. What is the bandwidth-delay product? If the
system data frames are 1000 bits in length, what is the utilization percentage of
the link?
Solution
The bandwidth-delay product is
1  106  20  10-3 = 20,000 bits
The system can send 20,000 bits during the time it takes for the data to go
from the sender to the receiver and then back again. However, the system
sends only 1000 bits. We can say that the link utilization is only 1000/20,000,
or 5%. For this reason, for a link with high bandwidth or long delay, use of
Stop-and-Wait ARQ wastes the capacity of the link.
Example 2
What is the utilization percentage of the link in Example 1 if the link uses GoBack-N ARQ with a 15-frame sequence?
Solution
The bandwidth-delay product is still 20,000. The system can send up to 15
frames or 15,000 bits during a round trip. This means the utilization is
15,000/20,000, or 75 percent. Of course, if there are damaged frames, the
utilization percentage is much less because frames have to be resent.
High-level Data Link Control Protocol
 HDLC is one of the first protocols that implements mechanisms of
ARQ
 Supports half-duplex and full-duplex mode on point-to-point links
 Uses three types of frames: information (I-frames), supervisory (Sframes) and unnumbered (U-frames)
 Only I frames carry information, S frames carry transport control
information and U frames are used for managing the link
HDLC Frame Structure
Flag
Address
Control
 Flag: 01111110, at start and end
 Physical Address: secondary
station (for multidrop
configurations)
 Information: the data to be
transmitted
 Frame check sequence (FCS):
16- or 32-bit CRC
Information
FCS
Flag
 Control: purpose or function of
frame
 Information frames: contain
user data
 Supervisory frames: flow/error
control (ACK/ARQ)
 Unnumbered frames: variety of
control functions (see p.220)
11.18
HDLC frame types
The Need for Bit Stuffing
 The flags show the receiver the start and the end of frame
 There is a problem if the flag appears in the middle of the
frame as a part of data
 The receiver will ”think” it is the end of frame
 A technique called “bit stuffing” is used to resolve this
problem
Bit Stuffing
 The sender stuffs redundant 0s
 Every time it encounters five 1s in a row, it inserts a redundant 0
 The redundant 0 tells the receiver that the sequence is not a flag
 The receiver removes all redundant 0s to restore the original frame
 Example: Bit stuff the following data:
0001111111110111100011111011
000111110111101111000111110011
Redundant 0s
11.24
Bit stuffing and removal
11.25
Bit stuffing in HDLC
PPP (Point-to-Point Protocol)
 Based upon HDLC
 Used for point-to-point access
 Common protocol used for connecting home users to the Internet (via
dial-up, DSL or cable modem or leased line)
 Defines the negotiation for establishment of the link
 Defines the protocol carried on the network layer
 Includes authentication and a field about the type of network protocol
carried within the frame
PPP Frame Format
Number of bytes in a field
1
1
Flag
Address
01111110 11111111
1
Control
00000011
1 or 2
variable
Protocol
Payload
2 or 4
CRC
1
Flag
01111110
 Physical Address field with all 1s indicate
broadcasting, i.e. that all stations accept the
frame
 Since the Address and Control fields are
constant, the two parties can negotiate to omit
them, thus saving 2 bytes
 Protocol field defines what is carried in the
payload field (user data or other information)
 CRC bits are error control bits