15-441 - Kesden

1
15-441 - Kesden

• Lecture 5/Spring 2007

2
ISO/OSI Reference Model

• Application
• Presentation
• Session
• Transport
• Network
• Data Link We are here
• Physical Weve been here

3
The Data Link Layer

• The physical layer was responsible for hiding the
  physical properties of the media.
• The network layer is responsible for moving
  packets from network to network.
• The link layer is responsible for getting packets
  from one machine to another on a particular
  network.
• For our purposes, a network is a collection of
  machines connected via a communications channel
  such that the connection logically appears as if
  it was a single wire or bus, regardless of the
  actual media or configuration.

4
Link Layer Design Issues

• Management of the media, generally
• Encoding
• Framing
• Error-detection/Error-correction maybe
• Flow control maybe

5
Management of the Media

• In many cases, there may be limitations about who
  can use the actual physical network connection
  and when.
• Broadcast media, such as ethernet, is the classic
  example.
• This issue belongs to a sublayer of the data link
  layer called the Medium Access Control (MAC)
  layer.

6
Link Types

• Broadcast
• Senders and receivers share medium all stations
  hear all transmissions
• Radio
• Sometimes wired, e.g. ethernet
• Point-to-point
• Fiber, RS232, USB (upstream vs. downstream)
• Switched
• Token ring

7
Address Types

• Static anointed, soft-configured
• Static anointed, more hard-wired
• Ethernet, 48 bits ????
• 24 bits per manufacturer
• 24 bits assigned by manufacturer
• Port/Position on switch
• Dynamic Anyone else use 45?
• Special addresses, e.g. designated broadcast

8
Encoding

• It is often the case that the physical layer has
  personality.
• For example, baseband signals send 1s and 0s as
  high and low voltages.
• But if the voltage doesnt change for a long
  time, timing tolerance becomes and issue.
• Long streams of 0s or 1s could lead to miscounted
  bits.
• Typically, it is the link layers responsibility
  to mitigate this type of physical layer property.
• This is done by encoding the bits in a way that
  is not subject to this type of problem.

9
NRZ (Non-Return to Zero)
0
1
0
0
1
1
0
0
1

• Easy thing to do
• Hard to count 0s or 1s
• Not necessarily balanced

10
Ethernet Manchester Encoding
0 rising transition 1 falling transition
0
0
1
1

• 1 transitions per bit, but twice as much
  bandwidth
• High-low pattern has good electrical properties
• Balanced signal no net DC voltage.
• This allows AC coupled power supply on receiver.
• If code had a DC bias, it would be lost in the
  transformer
• on the receiver side.

11
4B/5B Encoding

• Data encoded as symbols with 5 bit symbols
  representing 4 bit patterns
• 100Mbps data requires 125Mhz
• Each valid symbol has at least two 1s
• Guarantees transitions
• 16 data symbols
• 8 additional symbols used for control
• Idle
• Frame boundary
• FDDI is one example

12
Framing

• Physical layer is typically not error-free
• Link layer must discard correct and/or replace
  defective data, depending on quality of service.
• Typical approach is to break streams of 1s and
  0s into more managable pieces called frames
• Frames typically contain data bits and error
  correction or error detection bits
• Depending on the protocol, defective frames may
  be corrected (if possible) or discarded.
• Some link layer protocols might also handle
  retransmission of defective frames

13
Framing, Example
Which way do we lose more?
14
Example Point-To-Point Protocol (PPP), cont
Can be omitted by negotiation
1
variable
2 or 4
1
1 or 2
1
1
Flag Address Control Protocol
Payload Checksum Flag 01111110 11111111
00000011
01111110
The network layer packet
Always all 1s. All stations accept all packets
Usually as shown. Indicates unnumbered frame. Can
provide numbered frames and reliable link layer
especially useful for noisy lines
Indicates end of frame
Which network layer is above?
Indicates start of frame
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Example Point-To-Point Protocol (PPP), cont
Options agreed
ESTABLISHED
AUTHENTICATE
Authentication successful
Carrier detect
failed
NETWORK
DEAD
failed
NCP configuration
OPEN
Carrier dropped
TERMINATE
done
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Example Point-To-Point Protocol (PPP), cont

1
3
2
1
LCP Packet
To match request and reply
What type?
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LCP Packet Types
Name Direction Description
Configure-request Initiator?Responder Data has proposed options and values
Configure-ACK Initiator?Responder All proposed options and values accepted
Configure-NAK Initiator?Responder Data has rejected options
Configure-Reject Initiator?Responder Data has non-negotiable options
Terminate-Request Initiator?Responder Request to close line
Terminate-ACK Initiator?Responder OK, line is closed
Code-Reject Initiator?Responder Unknown request
Protocol-Reject Initiator?Responder Unknown protocol
Echo-request Initiator?Responder Please echo this frame (send back) (testing)
Echo-reply Initiator?Responder Here is the frame back (testing)
Discard-request Initiator?Responder Throw this frame away (testing)
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Error Correction vs. Error Detection

• Error correction is the ability to determine that
  a frame contains an error and then repair the
  error (without additional communication).
• Error detection is the ability to detect that a
  frame contains a defect, but not necessarily to
  have the ability to repair it.
• Error detection and error correction often
  involve adding additional bits called check bits
  or parity bits to the original bits of data.

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Simple Parity

• Supply extra bit to force sum to even or odd
• 1011, 1 even parity
• 1010,0 odd parity
• Old modems, ascii data
• 7 bits, character
• 1 bit, parity
• Quite weak

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Close Enough?

• Consider the following code
• 0 jump
• 1 run
• If 1 bit is in error, the message will be
  incorrect and misleading
• Now, consider the following code
• 00 jump
• 11 run
• Now, if only 1 bit is in error, the message wont
  make sense, but we know that there is an error.
• Okay, one more code
• 000 jump
• 111 run
• Now, if only 1 bit is in error, we can figure out
  which one it should be. If 2 bits are in error,
  we know that the codeword is defective, but dont
  know which bits are wrong.

21
Hamming Distance

• The Hamming Distance between two codewords is the
  number of bits that one would need to change to
  convert one into the other.
• The (minimum) Hamming distance of a code is the
  minimum Hamming Distance between any pair of
  codewords within the code.
• Hamming distance is important, because it gives
  us a way of determining how much error detection
  and how much error correction is possible for a
  given code.

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Thinking about Error Detection and Correction
T
T
T
If the targets are close enough, a miss might
hit the wrong one. If they are far enough apart,
a miss is more likely to land in between. If
they are really far apart, it is most likely that
the a miss will land closer to the intended
target than any other.
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Hamming Distance and EC/ED

• Like the example on the previous slide, Hamming
  distance measures how far two things (codewords)
  are apart.
• Remember that Hamming Distance measures the
  distance between two codewords by the number of
  bits that would need to change to convert one
  into another.
• This is a useful measure, because as long as the
  number of bits in error is less than the Hamming
  Distance, the error will be detected -- the
  codeword will be invalid.
• Similarly, if the Hamming distance between the
  codewords is more than double the number of bits
  in the error, the defective codeword will be
  closer to the correct one than to any other.

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Hamming Distance and EC/ED

• Review
• d bit errors can be detected if the Hamming
  Distance of the code is greater than d
• d bit errors can be corrected if the Hamming
  Distance of the code is greater than 2d

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How Many Check Bits?

• If we have a dense code with m message bits, we
  will need to add some r check bits to the message
  to put distance between the code words
• The total number of bits in the codeword
• n m r
• If we do this, each codeword will have n illegal
  codewords within 1 bit. (Flip each bit).
• To be able to correct an error, we need 1 more
  bit than this, (n 1) bits to make sure that
  1-bit errors will fall closer to one codeword
  than any other.

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Hammings Code

• Label the bits of the codeword from
  left-to-right, from 1 through n.
• Check bits are stored in power of two bit
  positions.
• Data bits are stored in other positions
• Each parity bit is used to force the sum of
  itself and the bits that it checks to an even
  number (or odd)
• Each bit is checked by one or more parity bits.
  Specifically, lets consider a bit index i. If
  we rewrite in terms of powers of 2, it is checked
  by those powers of two that contribute to the
  addition
• For example, 7 4 2 1 so bit 7 contributes
  to parity bits 4, 2, and 1.

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Hammings Code (Example)

• a _ _ 1 _ 1 0 0 _ 0 0
  1
• 1 2 3 4 5
  6 7 8 9 10 11
• 1 checks 3, 5, 7, 9, 11
• 1 1 0 0 1 3 set parity bit on to force
  even parity
• 2 checks 6, 7, 10, 11
• 0 0 0 1 1 set parity bit on to force
  even parity
• 4 checks 5, 6, 7
• 1 0 0 1 set parity bit on to force even
  parity
• 8 checks 9, 10, 11
• 0 0 1 1 set parity bit on to force even
  parity
• a 1 1 1 1 1 0 0 1 0
  0 1
• 1 2 3 4 5
  6 7 8 9 10 11

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Hammings Code (Ex.), cont.

• a 1 1 1 1 1 0 1 1 0 0
  1
• 1 2 3 4 5
  6 7 8 9 10 11
• 1 checks 3, 5, 7, 9, 11
• 1 1 1 0 1 4 parity should be 0, but it
  is 1. Count 1
• 2 checks 6, 7, 10, 11
• 0 1 0 1 2 parity bit should be 0, but
  isnt. Count 2, so count is 3
• 4 checks 5, 6, 7
• 1 0 1 2 parity bit should be 0, but
  isnt. Count 4, so count7
• 8 checks 9, 10, 11
• 0 0 1 1 parity bit should be 1 and is.
  Dont change count. Count is still 7
• So, if only 1 bit is in error, it is bit 7.

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Hammings Code (Ex.), cont.

• a 1 1 1 1 1 0 1 0 0 0
  1
• 1 2 3 4 5
  6 7 8 9 10 11
• 1 checks 3, 5, 7, 9, 11
• 1 1 1 0 1 4 parity should be 0, but it
  is 1. Count 1
• 2 checks 6, 7, 10, 11
• 0 1 0 1 2 parity bit should be 0, but
  isnt. Count 2, so count is 3
• 4 checks 5, 6, 7
• 1 0 1 2 parity bit should be 0, but
  isnt. Count 4, so count7
• 8 checks 9, 10, 11
• 0 0 1 0 parity bit should be 1 but is 0.
  Count 8, so count15.
• This makes no sense! More than 1 bit is in error.
  We cant fix it.

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Checksums

• Checksums are based on dividing binary
  polynomials, modulus 2.
• Both addition and subtraction are equal to XOR in
  modulus 2 arithmetic
• 10011011 11110000
• 11001010 10101111
• 01010001 01011111
• This can be used to perform long division.

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Checksums, cont.

• Given a message, we will add checksum bits
• These bits will be computed by dividing the
  message by a generator polynomial modulus 2.
• The remainder is the checksum
• The checksum is one bit smaller than the
  generator polynomial.
• Good polynomials wont divide the types of errors
  common in a particular channel

32
Checksum, cont.

• CRC-12 x12 x11 x3 x2 x1 1
• CRC-16 x16 x15 x2 1
• CRC-CCITT x16 x12 x5 1
• These can be represented as polynomials. For
  example, consider CRC-12
• 1 1 0 0 0 0 0 0 0 1 1 1 1

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Checksum, cont.

• 1 1 0 0 0 0 1 0 1 0
• 1 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 0 0 0
• 1 0 0 1 1
• 1 0 0 1 1
• 1 0 0 1 1
• 1 0 1 1 0
• 1 0 0 1 1
• 1 0 1 0 0
• 1 0 0 1 1
• 1 1 1 0

This remainder is the checksum.