Datornätverk A – lektion 7

Forts. Kapitel 9: SDH och SONET.

Kapitel 10: Felhantering.

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 ISP:s to share the same fiber cable independently.

Table 9.1 SONET ratesTable 9.1 SONET rates

STS OC Rate (Mbps) SPE (Mbps) User (Mbps)

STS-1STS-1 OC-1 51.84 50.12 49.536

STS-3STS-3 OC-3 155.52 150.336 148.608

STS-9STS-9 OC-9 466.56 451.008 445.824

STS-12STS-12 OC-12 622.08 601.344 594.432

STS-18STS-18 OC-18 933.12 902.016 891.648

STS-24STS-24 OC-24 1244.16 1202.688 1188.864

STS-36STS-36 OC-36 1866.23 1804.032 1783.296

STS-48STS-48 OC-48 2488.32 2405.376 2377.728

STS-192STS-192 OC-192 9953.28 9621.604 9510.912

Figure 9.14 STS multiplexing

Figure 9.12 Data rate

Figure 9.11 Frame format

SPE = Synchronous Payload Envelope

Figure 9.13 VT types

Data Link LayerData Link Layer

PART PART IIIIII

Position of the data-link layer

LLC and MAC sublayers

IEEE standards for LANs

Chapter 10

Error Detectionand

Correction

Data can be corrupted during transmission. For reliable

communication, errors must be detected and corrected.

NoteNote::

10.1 Types of Error10.1 Types of Error

Single-Bit Error

Burst Error

In a single-bit error, only one bit in the data unit has changed.

NoteNote::

10.1 Single-bit error

A burst error means that 2 or more bits in the data unit have changed.

NoteNote::

10.2 Burst error of length 5

Error detection uses the concept of redundancy, which means adding

extra bits for detecting errors at the destination.

NoteNote::

10.3 Redundancy

10.4 Detection methods

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).

NoteNote::

Example 1Example 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 3Example 3

Now suppose the word world in Example 1 is received by the receiver without being corrupted in transmission. 11101110 11011110 11100100 11011000 11001001The 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.

Simple parity check can detect all Simple parity check can detect all single-bit errors. It can detect burst single-bit errors. It can detect burst errors only if the total number of errors only if the total number of errors in each data unit is odd.errors in each data unit is odd.

NoteNote::

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.

NoteNote::

10.6 Two-dimensional parity

Example 4Example 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

17 1 7

. 1 5

2

5

0 3

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.

(Nämnare)Nominator (Täljare)

Reminder (Rest)

(Kvot)

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 = 00 XOR 1 = 11 XOR 0 = 11 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 quotient is 1 and one times the divisor results in this

Obtained by XOR-ing 1001 and 1101

The first bit in the numerator is 1. Then the first bit in the quotient is 1.

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 orderpolynomial

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 polynomialsTable 10.1 Standard polynomials

Name Polynomial Application

CRC-8CRC-8 x8 + x2 + x + 1 ATM header

CRC-10CRC-10 x10 + x9 + x5 + x4 + x 2 + 1 ATM AAL

ITU-16ITU-16 x16 + x12 + x5 + 1 HDLC

ITU-32ITU-32x32 + x26 + x23 + x22 + x16 + x12 + x11 + x10 + x8 + x7 + x5

+ x4 + x2 + x + 1LANs

Example 5Example 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.

Data bits to be sent CRC bits

k bits n 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 6Example 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.

10.12 Checksum

10.13 Data unit and checksum

The sender follows these steps:The sender follows these steps:

•The unit is divided into k sections, each of n bits.The unit is divided into k sections, each of n bits.

•All sections are added using one’s complement to get All sections are added using one’s complement to get the sum.the sum.

•The sum is complemented and becomes the checksum.The sum is complemented and becomes the checksum.

•The checksum is sent with the data.The checksum is sent with the data.

NoteNote::

Example1 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

• 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

Carry from column 1

Column: 7 6 5 4 3 2 1

Carry from column 2

Carry from column 3

Carry from column 4

Carry from column 5

SumChecksum

Example 7Example 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

00111001 ------------Sum 11100010

Checksum 00011101

The pattern sent is 10101001 00111001 00011101

Example 8Example 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.

The receiver follows these steps:The receiver follows these steps:

•The unit is divided into k sections, each of n bits.The unit is divided into k sections, each of n bits.

•All sections are added using one’s complement to get All sections are added using one’s complement to get the sum.the sum.

•The sum is complemented.The sum is complemented.

•If the result is zero, the data are accepted: otherwise, If the result is zero, the data are accepted: otherwise, rejected.rejected.

NoteNote::

Example 9Example 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.

Felrättande koder

FEC = Forward Error Correction = Felrättande koder.

Två typer:

1. Faltningskoder (convolutional codes). Ex:Vid Faltningskod med kodtakt (code rate) 1/3 infogas en

redundant bit mellan varje bit i nyttomeddelandet.

2. BlockkoderEx: Vid Read Salomon-kod med beteckningen RS(128,16), har man

128 bytes nyttodata och 16 bytes redundant felupptäckande kod i varje block.