Datorn

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Datornätverk A lektion 7

• Forts. Kapitel 9 SDH och SONET.
• Kapitel 10 Felhantering.

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Optical Hierarchies

• The old PCM hierarchy was non-synchronous
• Different multiplexors may have slightly
  different clock frequency.
• The whole hierarchy had to be unpacked in view to
  access or monitor a single telephone call, which
  was expensive.
• SDH and SONET use synchronous communication
• Clocked by a central master clock.
• SDH (Synchronous Digital Hierarchy)
• A standard for TDM in Europe
• SONET (Synchronious Optical NETwork)
• A standard for TDM used in United States
• IP-over-SDH/SONET allows several ISPs to share
  the same fiber cable independently.

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Table 9.1 SONET rates
STS OC Rate (Mbps) SPE (Mbps) User (Mbps)
STS-1 OC-1 51.84 50.12 49.536
STS-3 OC-3 155.52 150.336 148.608
STS-9 OC-9 466.56 451.008 445.824
STS-12 OC-12 622.08 601.344 594.432
STS-18 OC-18 933.12 902.016 891.648
STS-24 OC-24 1244.16 1202.688 1188.864
STS-36 OC-36 1866.23 1804.032 1783.296
STS-48 OC-48 2488.32 2405.376 2377.728
STS-192 OC-192 9953.28 9621.604 9510.912
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Figure 9.14 STS multiplexing
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Figure 9.12 Data rate
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Figure 9.11 Frame format
SPE Synchronous Payload Envelope
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Figure 9.13 VT types
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PART III
Data Link Layer
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Position of the data-link layer
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LLC and MAC sublayers
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IEEE standards for LANs
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Chapter 10
Error DetectionandCorrection
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Note
Data can be corrupted during transmission. For
reliable communication, errors must be detected
and corrected.
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10.1 Types of Error
Single-Bit Error Burst Error
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Note
In a single-bit error, only one bit in the data
unit has changed.
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10.1 Single-bit error
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Note
A burst error means that 2 or more bits in the
data unit have changed.
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10.2 Burst error of length 5
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Note
Error detection uses the concept of redundancy,
which means adding extra bits for detecting
errors at the destination.
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10.3 Redundancy
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10.4 Detection methods
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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).
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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
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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.
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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.
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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.
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10.6 Two-dimensional parity
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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


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10.7 CRC generator and checker
CRC Cyclic Redundency Check
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Vanlig division
(Kvot)
0 3
Nominator (Täljare)
5
17
1 7 . 1 5 2
(Nämnare)
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.
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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.

Examples 1011 XOR 0101 1110 1001 XOR 1101
0100
0 XOR 0 0 0 XOR 1 1 1 XOR 0 1 1 XOR 1 0
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10.8 Binary division in a CRC generator
The number of 0s is one less than the number of
bits in G (divisor)
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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
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10.8 Binary division in a CRC generator
Transmitted data 1 0 0 1 0 0 0 0 1
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10.9 Binary division in CRC checker
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Another Example
The transmitted data is 11010110111110
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10.11 A polynomial representing a divisor
7th orderpolynomial
8 bit divisor
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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
• 1x6 0x5 1x4 0x3 1x2 1x1 0x0
• x6 x4 x2 x

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Table 10.1 Standard polynomials
Name Polynomial Application
CRC-8 x8 x2 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
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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).
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How CRC Operates

• The sender wants to send k bits message
• The sender and the receiver must agree in advance
  on n1 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.

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How CRC Operates (Cont.)

• The redundant bits are chosen in such a way that
  the resulting kn bit string is exactly divisible
  (with a reminder0) 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

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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.
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10.12 Checksum
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10.13 Data unit and checksum
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Note

• The sender follows these steps
• The unit is divided into k sections, each of n
  bits.
• All sections are added using ones complement to
  get the sum.
• The sum is complemented and becomes the checksum.
• The checksum is sent with the data.

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Example
Column 7 6 5 4 3 2 1
Carry from column 5
1 0
1
1
1
1
0 0 1 1 0
1 0 0 0 1
1 1 0 0 1
1 0 1 1 1
1 0 0 0 1 1 1
1 0
0 1 0 0 1
1 0 1 1 0
Carry from column 4
Carry from column 3
Carry from column 2

• n5 bit checksum.
• 20 bit data gives k20/n4 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

Carry from column 1
Sum
Checksum
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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 ones
complement 10101001
00111001
------------Sum
11100010 Checksum 00011101 The pattern
sent is 10101001 00111001 00011101
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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.
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Note

• The receiver follows these steps
• The unit is divided into k sections, each of n
  bits.
• All sections are added using ones complement to
  get the sum.
• The sum is complemented.
• If the result is zero, the data are accepted
  otherwise, rejected.

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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
1 Sum 11000110 Complement
00111001 the pattern is corrupted.
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Felrättande koder

• FEC Forward Error Correction Felrättande
  koder.
• Två typer
• Faltningskoder (convolutional codes).
• ExVid Faltningskod med kodtakt (code rate) 1/3
  infogas en redundant bit mellan varje bit i
  nyttomeddelandet.
• Blockkoder
• Ex Vid Read Salomon-kod med beteckningen
  RS(128,16), har man 128 bytes nyttodata och 16
  bytes redundant felupptäckande kod i varje block.