1. Datornätverk A – lektion 7
Forts. Kapitel 9: SDH och SONET.
Kapitel 10: Felhantering.

2. Figure 6.18 PCM hierarchy – Circuit Oriented TDM

3. Table 6.2 The European PCM hierarchy
E Line
Rate (Mbps)
Voice Channels
E-1
2.048 30
E-2
8.448
120
E-3
34.368
480
E-4
1920

4. 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.

5. Note:
SONET and SDH are synchronous TDM systems controlled by a master clock.

6. Figure A SONET

7. Figure Frame format

8. Table 9.1 SONET rates STS OC Rate (Mbps) SPE (Mbps) User (Mbps) STS-1
51.84
50.12
49.536
STS-3
OC-3
155.52
STS-9
OC-9
466.56
STS-12
OC-12
622.08
STS-18
OC-18
933.12
STS-24
OC-24
STS-36
OC-36
STS-48
OC-48
STS-192
OC-192

9. Figure Data rate

10. Figure VT types

11. Figure Data rate

12. SPE = Synchronous Payload Envelope
Figure Frame format
SPE = Synchronous Payload Envelope

13. Figure VT types

14. PART III
Data Link Layer

15. Position of the data-link layer

16. LLC and MAC sublayers

17. IEEE standards for LANs

18. Error Detection and Correction
Chapter 10
Error Detection and Correction

19. Note:
Data can be corrupted during transmission. For reliable communication, errors must be detected and corrected.

20. Types of Error
Single-Bit Error
Burst Error

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

22. Single-bit error

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

24. Burst error of length 5

25. Note:
Error detection uses the concept of redundancy, which means adding extra bits for detecting errors at the destination.

26. Redundancy

27. Detection methods

28. 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).

29. Example 1
Suppose the sender wants to send the word world. In ASCII (7-bit code) the five characters are coded as
Even parity is used. The following shows the actual bits sent:

30. Example 3
Now suppose the word world in Example 1 is received by the receiver without being corrupted in transmission.
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.
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.

31. 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.

32. 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.

33. 10.6 Two-dimensional parity

34. Example 4 Suppose the following block is sent:
However, it is hit by a burst noise of length 8, and some bits are corrupted.
When the receiver checks the parity bits, some of the bits do not follow the even-parity rule and the whole block is discarded.

35. CRC = Cyclic Redundency Check
CRC generator and checker
CRC = Cyclic Redundency Check

36. ”Vanlig” division (Nämnare)
(Kvot)
0 3 5
Nominator (Täljare)
1 7
. 1 5 2 17
(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.

37. Modulo 2 Arithmetic Examples: 1011 XOR 0101 = 1110
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

38. 10.8 Binary division in a CRC generator
The number of 0s is one less than the number of bits in G (divisor)

39. 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

40. 10.8 Binary division in a CRC generator
Transmitted data:

41. 10.9 Binary division in CRC checker

42. Another Example
The transmitted data is

43. 7th order polynomial 8 bit divisor
A polynomial representing a divisor
7th order polynomial
8 bit divisor

44. 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: 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

45. 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

46. 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).

47. 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

48. 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

49. 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, percent of the time, burst errors with a length of 12 or more.

50. Checksum

51. Data unit and checksum

52. 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.

53. Example n=5 bit checksum. 20 bit data gives k=20/n=4 sections (rows).
Column:
Carry from column 5 1
Example
Carry from column 4
Carry from column 3
Carry from column 2
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
Sum
Checksum

54. Example 7
Suppose the following block of 16 bits is to be sent using a checksum of 8 bits.
The numbers are added using one’s complement
Sum
Checksum
The pattern sent is

55. Example 8
Now suppose the receiver receives the pattern sent in Example 7 and there is no error.
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.
Sum
Complement means that the pattern is OK.

56. 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.

57. Example 9
Now suppose there is a burst error of length 5 that affects 4 bits.
When the receiver adds the three sections, it gets
Partial Sum
Carry
Sum
Complement the pattern is corrupted.

58. Felrättande koder FEC = Forward Error Correction = Felrättande koder.
Två typer:
Faltningskoder (convolutional codes).
Ex:Vid 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.