CS144 7-2 Bit Errors

Introduction to Computer Networking, Stanford University
https://lagunita.stanford.edu/courses/Engineering/Networking-SP/SelfPaced/about

Unit 7: Lower Layers 중 Bit Errors 파트 수업 필기 정리

 

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(recall) Shannon Limit

• the capacity of a communication channel
• Bandwidth * log₂(1 + S/N)
  • Bandwidth typically fixed
  • SNR:
    Possible data rate bounded by the Signal to Noise Ratio
    • Stronger signal or lower noise → transmit data faster
  • theoretical limit
    • don't necessarily know how to achieve it
• Stronger signal = you can transmit data faster
  • Shorter symbols
    • Transmit symbols for shorter periods of time
  • More bits per symbol
    • make constellation denser

Bit Errors

due to noise, some symbols are misrecorded or misunderstood on constellation

if the constellation is sparse enough, then it would be okay
but when the constellation is dense when compared to the degree of noise, it would cause bit errors (misunderstanding)

 

BER Curves

• a given modulation scheme and SNR → able to compute the expected BER (Bit Error Rate)
• BER never reaches zero
  • so the most efficient way to transmit data:
    send the right number of bits per symbol
    → directly translate bits in a packet into bits in symbols
  • Bit Error Possibility never reaches zero!
• In practice, to directly map bits to symbols,
  the expected data throughput will be far below shannon limit

Chips(Physical layer) vs. Bits(Link layer)

• physical layer must deal with noise → prevent chip errors
  • denser modulation → higher throughput
  • sparser modulation → fewer errors
  • High-power transmitters → higher throughput

 

Coding

Add a little redundancy at the physical layer to improve link layer throughput of the system

 

Coding gain

the ratio of bits at link layer → bits at physical layer

• 1/2 code: each link layer bit is 2 physical layer bits

• 3/4 code: each 3 link layer bit is 4 physical layer bits

 

Calculating Data Rate

bitrate = bits/symbol * symbol rate * coding rate

Example 1

• 802.15.4
• Bitrate: 250kbps in the link layer
• Coding rate: 16 chips of 2 bits = 4bits
• how many symbols are we transmitting per second?
  8 * 250 kbps = 2Mbps,
  and each physical layer has 2bits,
  each link layer has 1bits → 1M symbols

Example 2

• a simplified form of 64-QAM modulation which supports a bit rate of 150 Mbps
• Bit rate: 150Mbps
• Coding gain = 5/6
  link layer 5, physical layer 6
• how many symbols from link layer transmitted?
  150 = 5/6