1. EEC-484/584 Computer Networks
Lecture 8
Wenbing Zhao
(Part of the slides are based on materials supplied by Dr. Louise Moser at UCSB and Prentice-Hall)

2. Outline Data Link layer Error Detection and Correction
Elementary data link protocols
DLL
Data Link
Medium Access Control (MAC)
We Study
This SubLayer in This Lecture
Spring Semester 2007
EEC-484/584: Computer Networks

3. Error Detection and Correction
Causes of errors
Transmission errors on phone lines due to thermal noise
Data transmission errors due to impulse noise
Signals are separated, distorted, recombined
Crosstalk between physically adjacent wires
Compression and decompression
Receiver out of synch with sender
Errors usually occur in bursts
Spring Semester 2007
EEC-484/584: Computer Networks

4. Error-Correcting Codes
n-bit codeword – an n-bit unit containing data and check bits
m bits of data, r bits redundant/check bits (n = m+r)
How to measure the differences between two codewords (num of different bits)
Using exclusive OR and counting number of 1 bits in the result
Spring Semester 2007
EEC-484/584: Computer Networks

5. Error-Correcting Codes
Hamming distance – number of bit positions in which two codewords differ
If two codewords are a Hamming distance d apart, it will require d single-bit errors to convert one into the other
Spring Semester 2007
EEC-484/584: Computer Networks

6. Error-Correcting Codes
Complete code
Complete list of all legal codewords: 2m possible data messages
Recall that there are m bits of data
Hamming distance of the complete code
Find two codewords whose Hamming distance is minimum
, but not all 2n possible codewords are used
Spring Semester 2007
EEC-484/584: Computer Networks

7. Error-Detection Codes
A distance d+1 code can detect up to d errors, why?
If there are d+1 errors, one valid codeword might be turned into another valid codeword
≤ d errors will change a valid codeword into an illegal codeword  can be detected!
Spring Semester 2007
EEC-484/584: Computer Networks

8. Error-Correcting Codes
To correct d errors, need a distance 2d+1 code
Legal codewords are so far part that even with d changes, original codeword is still closer than any other codeword, so it can be uniquely determined
Spring Semester 2007
EEC-484/584: Computer Networks

9. Error-Correcting Codes: Example
Consider a code with only four valid codewords
, , ,
This code has a distance 5  can correct double errors
If arrives, receiver knows the original must have been
However, if triple error changes to , the error will not be corrected properly
Spring Semester 2007
EEC-484/584: Computer Networks

10. EEC-484/584: Computer Networks
Parity Bit
Parity bit – a single bit is appended to the data
Parity bit is chosen so that number of 1 bits in the codeword is even or odd
Example: Given
With even parity 
With odd parity 
A code with a single parity bit has a distance 2
Since any single-bit error produces a codeword with wrong parity  can be used to detect single bit errors
Spring Semester 2007
EEC-484/584: Computer Networks

11. Error-Detecting Codes
If a single parity bit is appended to a block, error detecting probability is only 0.5 if burst error occurs (why?)
This can be improved by treating a block as a matrix, n bits wide and k bits high,
A parity bit is computed for each column and affixed to the matrix as the last row
The matrix is transmitted one row at a time
Probability of accepting bad block is 2-n
Spring Semester 2007
EEC-484/584: Computer Networks

12. Error-Detecting Codes: CRC
Polynomial code, also known as CRC (Cyclic Redundant Code)
Treat bit string as polynomial with 0 and 1 coefficients
m-bit frame: M(x) = bm-1xm-1 + … + b0
E.g.: => M(x) = x7 + x6 + x4 + x3 + x1
Use modulo 2 arithmetic
No carries or borrows: XOR
The degree of a polynomial is the maximum of the degrees of all terms in the polynomial
Spring Semester 2007
EEC-484/584: Computer Networks

13. EEC-484/584: Computer Networks
Cyclic Redundant Code
Sender and receiver agree on generator polynomial G(x) (High & low order bits must be 1)
For a frame with m bits corresponding to M(x), m > deg G(x) = r
Append checksum to end of frame so polynomial T(x) corresponding to checksummed frame is divisible by G(x)
When receiver gets checksummed frame, divides T(x) by G(x)
If remainder R(x) != 0, then transmission error
Spring Semester 2007
EEC-484/584: Computer Networks

14. Algorithm to Compute CRC Checksum
Let m = deg M(x), r = deg G(x)
Append r 0 bits to lower-order end of frame: xrM(x)
Divide bit string corresponding to xrM(x) by bit string corresponding to G(x)
Subtract remainder R(x) from bit string corresponding to xrM(x), result is checksummed frame. Let T(x) be its polynomial
xrM(x) = Q(x)G(x) + R(x)
xrM(x) – R(x) = Q(x)G(x) = T(x)
Spring Semester 2007
EEC-484/584: Computer Networks

15. EEC-484/584: Computer Networks
Compute CRC Checksum
XOR
Spring Semester 2007
EEC-484/584: Computer Networks

16. International Standard Polynomials
CRC-12 G(x) = x12 + x11 + x3 + x2 + x1 + 1
Used for 6-bit characters
CRC-16 G(x) = x16 + x15 + x2 + 1 CRC-CCITT G(x) = x16 + x12 + x5 + 1
Used for 8-bit characters
CRC-32 G(x) = x32 + x26 + x23 + x22 + x16 + x11 + x10 + x8 + x7 + x5 + x4 + x2 + x1 + 1
Used in IEEE 802
Detects all bursts of length 32 or less and all bursts affecting an odd number of bits
No need to remember these generator polynomials
Spring Semester 2007
EEC-484/584: Computer Networks

17. EEC-484/584: Computer Networks
Exercise
Q5. To provide more reliability than a single parity bit can give, an error-detecting coding scheme uses one parity bit for checking all the odd-numbered bits and a second parity bit for all the even-numbered bits. What is the Hamming distance of this code?
Spring Semester 2007
EEC-484/584: Computer Networks

18. EEC-484/584: Computer Networks
Exercise
Q6. A bit stream is transmitted using the standard CRC method described in the text. The generator polynomial is x Show the actual bit string transmitted. Suppose the third bit from the left is inverted during transmission. Show that this error is detected at the receiver's end.
Spring Semester 2007
EEC-484/584: Computer Networks

19. Elementary Data Link Protocols*
An Unrestricted Simplex Protocol
A Simplex Stop-and-Wait Protocol
Simplex Protocols for a Noisy Channel
*Materials taken from:
Spring Semester 2007
EEC-484/584: Computer Networks

20. Data Structure and Library Routines for DLL
Routines for host communications: transfer an array of data between host system and DLL:
FromHost(message)
Fetch message (to be transmitted) from host
ToHost(message)
Deliver message (received) to host where message is an array of information to be passed
Spring Semester 2007
EEC-484/584: Computer Networks

21. Data Structure and Library Routines for DLL
Physical layer to DLL interface: routines that transfer data frames between physical layer and data link layer 
SendFrame (frame) send a frame
GetFrame (frame) get a frame
Spring Semester 2007
EEC-484/584: Computer Networks

22. Data Structure and Library Routines for DLL
Frame: a data structure composed of four fields
kind: variable of type FrameKind identifies the type of frame (control or data frame)
seq: the sequence number of this frame (if any)
ack: sequence number of frame to acknowledge (if any)
info: the data message (if any)
Spring Semester 2007
EEC-484/584: Computer Networks

23. Data Structure and Library Routines for DLL
StartTimer: starts an internal timer
StopTimer: stops the timer  
WaitEvent(event): is called by the receiver to wait for an event, where the value returned by event indicates the type of event which occurred:
FrameArrival to indicate the arrival of an error free frame
ChSumErr to indicate a checksum error occurred on the frame
TimeOut the timer has 'timed out'
Spring Semester 2007
EEC-484/584: Computer Networks

24. Unrestricted Simplex Protocol
Assumptions
messages one way only
physical channel with no errors
both hosts are always ready (to receive and transmit)
A communications protocol is the set of rules which define how the flow of data between the transmitter and receiver is controlled.
Spring Semester 2007
EEC-484/584: Computer Networks

25. Unrestricted Simplex Protocol
Sender pseudo code
LOOP forever
FromHost(frame.info) frame.kind = data SendFrame(frame)
ENDLOOP
Spring Semester 2007
EEC-484/584: Computer Networks

26. Unrestricted Simplex Protocol
Receiver pseudo code
LOOP forever
WaitEvent (event) /*wait for FrameArrival */
GetFrame (Rfraxne) /* get info frame from receiver */
ToHost(Rframe. info) /* pass message to host */
ENDLOOP
Only possible event is FrameArrival and type of frame received is data
Spring Semester 2007
EEC-484/584: Computer Networks

27. Unrestricted Simplex Protocol
message a3 is corrupt when passed to host B and message a6 is
totally lost. In addition, if a slow receiver is connected to a fast transmitter,
data would be lost due to overflow
Spring Semester 2007
EEC-484/584: Computer Networks

28. Simplex Stop and Wait Protocol
Add flow control: receiver provide feedback
Sender pseudo code
LOOP forever
FromHost (Sframe.info) /*get message from host */ Sframe.kind = data /* set up data frame with message */
SendFrame (Sframe) /* and transmit frame */
WaitEvent (event) /* STOP and WAIT for ack frame */
GetFrame (Rframe) /* get it and discard it */
ENDLOOP
Only possible event is FrameArrival and type of frame received is ack.
Spring Semester 2007
EEC-484/584: Computer Networks

29. Simplex Stop and Wait Protocol
Receiver pseudo code
LOOP forever
WaitEvent (event) /* wait for FrameArrival */
GetFrame (Rframe) /* get the frame from receiver */
ToHost (Rframe.info) /* pass message to host */
Sframe.kind = ack /* build ack frame */
SendFrame (sframe) /* and transmit frame */
ENDLOOP
Only possible event is FrameArrival and type of frame received is data.
Spring Semester 2007
EEC-484/584: Computer Networks

30. Simplex Stop and Wait Protocol
Effect of a damaged frame: passes a corrupt message to the host
Effect of a lost message or ack: causes lockup - A waiting for ack from B and B waiting for data from A
Spring Semester 2007
EEC-484/584: Computer Networks

31. Simplex ARQ Protocol for a Noisy Channel
Dealing with lost of data frame with retransmission
Receiver: check event, if it is not FrameArrival ignore it
Sender: send data frame and if an ack is not received within a certain time retransmit it
Need two new functions
StartTimer: starts an internal timer
StopTimer: stops the timer
If the timer 'times out’ WaitEvent returns an event value of TimeOut
Spring Semester 2007
EEC-484/584: Computer Networks

32. Simplex ARQ Protocol for a Noisy Channel
Sender pseudo code
LOOP forever
FromHost (Sframe.info) /* get message from host */
Sframe.kind = data /* set up data frame with message */ REPEAT /* until ack arrives */
SendFrame (Sframe) /* and transmit frame */ StartTimer /* start the timre */
WaitEvent (event) /* stop and wait for ack frame */
UNTIL event = FrameArrival /* ack frame arrived ? */
StopTimer /* stop the timer */
GetFrame (Rframe) /* get ack frame and discard it */
ENDLOOP
In this case event may be FrameArrival or TimeOut
Spring Semester 2007
EEC-484/584: Computer Networks

33. Simplex ARQ Protocol for a Noisy Channel
Receiver pseudo code
LOOP forever
REPEAT /* until frame OK */
WaitEvent(event) /* wait for FrameArrival */ GetFrame(Rframe) /* get the frame from receiver */
UNTIL event = FrameArrival /* data frame arrived ? */
ToHost(Rframe.info) /* pass message to host */
Sframe.kind = ack /* build ack frame */
SendFrame(Sframe) /* and transmit frame */
ENDLOOP
In this case event maybe FrameArrival or ChSumErr
Spring Semester 2007
EEC-484/584: Computer Networks

34. Simplex ARQ Protocol for a Noisy Channel
Problem: duplicate delivery
Spring Semester 2007
EEC-484/584: Computer Networks

35. Simplex ARQ Protocol for a Noisy Channel
Problem: duplicate delivery
Spring Semester 2007
EEC-484/584: Computer Networks

36. Simplex ARQ Protocol for a Noisy Channel
Problem: duplicate delivery
Spring Semester 2007
EEC-484/584: Computer Networks

37. Simplex ARQ Protocol with Sequence Numbers for a Noisy Channel
Each frame must carry a sequence number
Sender: sets up the seq number in the data frame and keeps transmitting it until it gets an ack
Receiver: when it gets a data frame with a particular sequence number:
sends an acknowledgement frame
checks that the sequence number of the frame is the expected sequence number: if so it is passed to the host and the expected sequence number incremented else the frame is discarded
Spring Semester 2007
EEC-484/584: Computer Networks

38. Simplex ARQ Protocol with Sequence Numbers for a Noisy Channel
Sender psuedo code
SeqSend = 0 LOOP forever
FromHost(Sframe.info) Sframe.kind = data Sframe.seq = SeqSend REPEAT
SendFrame (Sframe) StartTimer WaitEvent(event)
UNTIL event FrameArrival SeqSend = SeqSend StopTimer GetFrame(Rframe)
ENDLOOP
/* initial sequence number */  
/* get message from host */ /*set up data frame with message */ /* set up sequence number */ /* until ack arrives */
/* transmit frame */ /* start the timer */
/* STOP and WAIT for ack frame */
/* ack frame arrived? */ /* set up next sequence number */ /* stop the timer */
/* get it and discard it */
In this case event may be FrameArrival or TimeOut
Spring Semester 2007
EEC-484/584: Computer Networks

39. Simplex ARQ Protocol with Sequence Numbers for a Noisy Channel
Receiver pseudo code
SeqExpected = 0 LOOP forever
REPEAT
WaitEvent (event) GetFrame (Rframe)
UNTIL event = FrameArrival if (SeqExpected = Rframe.seq) {     ToHost (Rframe. info)     SeqExpected = SeqExpected } Sframe.kind = ack SendFrame (Sframe)
ENDLOOP
/* initial sequence number */  
/* until frame OK */
/* wait for Frame Arrival */ /* get the frame from receiver */
/* frame OK? */ /* yes, frame expected? */
/* yes, pass message to host */ /* next sequence number */
/* build ack frame */ /* and transmit frame */
In this case event may be FrameArrival or ChSumErr
Spring Semester 2007
EEC-484/584: Computer Networks

40. Simplex ARQ Protocol with Sequence Numbers for a Noisy Channel
The sequence numbers for this protocol can be held in a single bit with a sequence of frames having the numbers etc.
Spring Semester 2007
EEC-484/584: Computer Networks

41. Simplex ARQ Protocol with Sequence Numbers for a Noisy Channel
Spring Semester 2007
EEC-484/584: Computer Networks

42. Simplex ARQ Protocol with Sequence Numbers for a Noisy Channel
Spring Semester 2007
EEC-484/584: Computer Networks

43. Simplex ARQ Protocol with Sequence Numbers for a Noisy Channel
Spring Semester 2007
EEC-484/584: Computer Networks

44. Simplex ARQ Protocol with Sequence Numbers for a Noisy Channel
This protocol still has a problem
Identify the problem
How to fix it?
Spring Semester 2007
EEC-484/584: Computer Networks