Recap: Byte Count

Recap: Byte Count

• Frame begins with a count of the number of bytes in it
  • Simple, but difficult to resynchronize after an error

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Error Correction

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Codewords

• A frame consists of m data (message) bits and r redundant (check) bits.

• n-bit codewords with n =m+r

• ASCII code for “A”: 1000001
• codeword for “A”: 10000010 (r=1)

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Error Bounds – Hamming distance

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Error Bounds – Hamming distance

Example with 2 codewords:

• Codeword #1: 1 0 0 0 1 0 0 1

• Codeword #2: 1 0 1 1 0 0 0 1

• Hamming distance is 3. The number of bit positions in which two codewords differ

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Error Detection and Correction

Hamming distance

Step 1: Ensure the two strings are of equal length.

• Codeword #1: 1 0 0 0 1 0 0 1
• Codeword #2: 1 0 1 1 0 0 0 1

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Error Detection and Correction

Hamming distance

Step 2: Compare the first two bits in each codeword (XOR them). If they are the same, record a “0” for that bit. If they are different, record a “1” for that bit. Repeat the process for the remaining bits.

• Codeword #1: 1 0 0 0 1 0 0 1
• Codeword #2: 1 0 1 1 0 0 0 1
• Record: 0 0 1 1 1 0 0 0

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Error Detection and Correction

Hamming distance

Step 3: Add all the ones and zeros in the record together to obtain the Hamming distance.

• Hamming distance = 0 + 0 + 1 + 1 + 1 + 0 + 0 + 0 = 3
• OR, count the number of 1s in the record. Three 1 bits in the record. i.e., Hamming distance is 3

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Hamming Codes

Encoding:

• We number the data bits starting from one and skipping the powers of two. The powers of two are reserved for parity bits. The rest are for message bits.

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Hamming Codes

Decoding:

• Calculate all parities. If they are all OK, there was no error. If not, add up the positions of the incorrect ones- this gives us the position of the error

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Error Correction – Hamming code

The Hamming code gives a simple way to add check bits and correct up to a single bit error:

• Check bits are parity over subsets of the codeword
• Recomputing the parity sums (syndrome) gives the position of the error to flip, or 0 if there is no error

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Error Correction – Hamming code

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Error Correction – Hamming code

0 0 1 0 0 0 0 1 0 0 1 (original codeword)

0 0 1 0 1 0 0 1 0 0 1 (received codeword)

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Error Correction – Hamming code

0 0 1 0 0 0 0 1 0 0 1 (original codeword)

• step #1: number the bits

1 2 3 4 5 6 7 8 9 10 11

0 0 1 0 1 0 0 1 0 0&nbsp&nbsp 1&nbsp (received codeword)

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Error Correction – Hamming code

0 0 1 0 0 0 0 1 0 0 1 (original codeword)

• step #2: allocate parity bits and message bits- powers of 2 bits are parity bits and the rest are message bits

p1 p2 m3 p4 m5 m6 m7 p8 m9 m10 m11

0 &nbsp 0 &nbsp 1 &nbsp &nbsp 0 &nbsp &nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp&nbsp&nbsp&nbsp 1 &nbsp&nbsp&nbsp (received codeword)

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Error Correction – Hamming code

0 0 1 0 0 0 0 1 0 0 1 (original codeword)

• step #3: finding the parity bits

p1 p2 m3 p4 m5 m6 m7 p8 m9 m10 m11

0 &nbsp 0 &nbsp 1 &nbsp &nbsp 0 &nbsp &nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp&nbsp&nbsp&nbsp 1 &nbsp&nbsp&nbsp

• Finding p1:
  • Count one bit and skip one, starting from p1 but not including p1 value.
  • Add the 1s. If the result is even then p1 parity is 0, if the result is odd then p1 parity is 1.
  • p1 is? 1 1 0 0 1 &rightarrow; 1

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Error Correction – Hamming code

0 0 1 0 0 0 0 1 0 0 1 (original codeword)

• step #3: finding the parity bits

p1 p2 m3 p4 m5 m6 m7 p8 m9 m10 m11

0 &nbsp 0 &nbsp 1 &nbsp &nbsp 0 &nbsp &nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp&nbsp&nbsp&nbsp 1 &nbsp&nbsp&nbsp

• Finding p2:
  • Count two bits and skip two, starting from p2 but not including p2 value.
  • Add up the result. If the result is even then p2 parity is 0, if the result is odd then p2 parity is 1
  • p2 is? 1 0 0 0 1 &rightarrow; 0

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Error Correction – Hamming code

0 0 1 0 0 0 0 1 0 0 1 (original codeword)

• step #3: finding the parity bits

p1 p2 m3 p4 m5 m6 m7 p8 m9 m10 m11

0 &nbsp 0 &nbsp 1 &nbsp &nbsp 0 &nbsp &nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp&nbsp&nbsp&nbsp 1 &nbsp&nbsp&nbsp

• Finding p4:
  • Count four bits and skip four, starting from p4 but not including p4 value.
  • Add up the result. If the result is even then p4 parity is 0, if the result is odd then p4 parity is 1.
  • p4 is ? 1 0 0 - - &rightarrow; 1

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Error Correction – Hamming code

0 0 1 0 0 0 0 1 0 0 1 (original codeword)

• step #3: finding the parity bits

p1 p2 m3 p4 m5 m6 m7 p8 m9 m10 m11

0 &nbsp 0 &nbsp 1 &nbsp &nbsp 0 &nbsp &nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp&nbsp&nbsp&nbsp 1 &nbsp&nbsp&nbsp

• Finding p8:
  • Count eight bits and skip eight, starting from p8 but not including p8 value.
  • Add up the result. If the result is even then p8 parity is 0, if the result is odd then p8 parity is 1.
  • p8 is ? 0 0 1 - - &rightarrow; 1

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Error Correction – Hamming code

0 0 1 0 0 0 0 1 0 0 1 (original codeword)

• step #4: compare our result with the received parity bits.

0 &nbsp 0 &nbsp 1 &nbsp &nbsp 0 &nbsp &nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp 1 &nbsp&nbsp 0 &nbsp&nbsp 0 &nbsp&nbsp&nbsp&nbsp&nbsp 1 &nbsp&nbsp&nbsp

• p1 is 0 1 1 0 0 1 → 1 ✘
• p2 is 0 1 0 0 0 1 → 0 ✔
• p4 is 0 1 0 0 - - → 1 ✘

• p8 is 1 0 0 1 - - → 1 ✔

• p1+p4 &rightarrow; in position 5

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Summary

• Link layer services

• Data Framing

• Error detection and correction

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MAC Layer

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Outline

• Elements of wireless network
• Wireless links, characteristics, and types
• IEEE 802.11 wireless LANs (“Wi-Fi”) and features
  • Hidden and exposed terminal
  • Wireless LAN standards & architecture
• Channeling, association and scanning
• IEEE 802.11 MAC protocol
• CSMA/CA
• IEEE 802.11 framing

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Elements of a wireless network

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Elements of a wireless network

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Elements of a wireless network

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Elements of a wireless network

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Elements of a wireless network

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Elements of a wireless network

Ad hoc mode

• No base stations
• Nodes can only transmit to other nodes within link coverage
• Nodes organize themselves into a network: route among themselves

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IEEE 802.11 Wireless LAN

• 802.11b, 802.11a, 802.11g, 802.11n (multiple antennae)…
• All use CSMA/CA for multiple access
• All have base-station and ad-hoc network versions

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Characteristics of selected wireless links

Standard	Frequency Range	Data Rate
802.11b	2.4 GHz	Up to 11 Mbps
802.11a	5 GHz	Up to 54 Mbps
802.11g	2.4 GHz	Up to 54 Mbps
802.11n	2.5 and 5 GHz	Up to 450 Mbps
802.11ac	5 GHz	Up to 1300 Mbps

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Wireless Link Characteristics

Important differences from wired link:

• Decreasing signal strength: radio signal attenuates as it propagates through matter (path loss)
• Interference from other sources: standardized wireless network frequencies (e.g., 2.4 GHz) shared by other devices (e.g., phone); devices (motors) interfere as well
• Multipath propagation: radio signal reflects off objects ground, arriving at destination at slightly different times

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Signals

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Properties of signals

Here:

• A: amplitude
• f: frequency, the number of oscillations (in Hz)
• ω = 2πf: angular frequency
• φ: phase, specifies position at t = 0

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Example: wired connection

• High and low voltages give a distinguishable waveform

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• Noise in the signal needs to be removed
• translate into a binary signal (only two states)

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Wireless connection

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• Generated by oscillating electic fields
• In the receiver the radio singla create a tiny voltage which can be measured

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Wireless network characteristics

Hidden terminal problem

• Hidden terminals are senders that cannot sense each other but nonetheless collide at intended receiver

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• B, A hear each other
• B, C hear each other
• A, C can not hear each other means A, C unaware of their interference at B

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Signal Attenuation

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• B, A hear each other
• B, C hear each other
• A, C can not hear each other interfering at B

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Exposed Terminals

Exposed terminals are senders who can sense each other but still transmit safely (to different receivers) Desirably concurrency; improves performance B ↔ A and C ↔ D are exposed terminals

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Roadmap

• Elements of wireless network
• Wireless links, characteristics, and types
• IEEE 802.11 wireless LANs (“Wi-Fi”) and features
  • Hidden and exposed terminal
  • Wireless LAN standards & architecture
• Channeling, association and scanning
• IEEE 802.11 MAC protocol
  • CSMA/CA
  • IEEE 802.11 framing