Computer Networking Lecture Notes

2013 November 12 • Digital Modulation and Multiplexing

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Outline

• Baseband transmission.
  • Digital coding.
  • Bandwidth, clocking, and balance.
• Passband transmission.
  • Amplitude, frequency, and phase modulation.
• Signal multiplexing.
  • Frequency, time, and code.

Problem

• Copy a bit stream from one system to another.

• 

• Assume for the moment twisted pair between systems.
• How do systems A and B turn the wire in to a channel to carry the bits?

Bit Encoding

• Do the obvious thing: use two signals to represent the two bits.

  

• t_b sec/bit, 1/t_b bits/sec, maximum frequency = 1/2t_b Hz.
• Unipolar non-return to zero (UNRZ).

Line Encoding

• A line encoding translates from a bit stream to a transmission signal.

• The translation is the line code.
• The receiver translates the transmitted signal back into a bit stream.
  • Line encoders and decoders are not symmetric.

Sampling

• Line decoding translates a digital transmission back into a bit stream.
  • “Digital”: finite levels.
• Sampling regularly observes the transmitted signal to recover the bits.

  

Synchronization

• It is crucial that the line encoder and decoder agree on t_b sec/bit.

  

• Agreeing and maintaining agreement is difficult.

Clocking

• An explicit clock provides one solution.

• Expensive, and doesn’t scale.
• There’s already a signal going between systems.
  • Can that signal be exploited to provide synchronization?

Adding A Clock

Don’t observe levels, observe level changes. The transition is the clock tick.

Self-Clocking Codes

• Codes that include a clock are self-clocking (self-synchronizing).

  

• This is the Manchester encoding.

Coding Efficiency

• Manchester coding needs twice the bandwidth of NRZ coding.
  • B bits/sec needs B Hz.
• Digital signals can be n-valued, not just 2-valued.
  • Each value is known as a symbol.
• One of n symbols can encode ⌈log₂ n⌉ bits.
  • The remaining n - 2^{⌈log₂ n⌉} symbols can be used for control or status.

Multi-Level Example

	Use five symbols to encode two bits. One symbol is for status.
	bit rate = 2 bit/sym · s sym/sec.

Transmission Rates

• Given s sym/sec and b bits/sym,

  bit rate	=	s sym/sec · b bits/sym
  	=	sb bits/sec

• The symbol rate s sym/sec is also known as the baud rate.
  • Beloved by those that remember modems, or RS-232.
• The symbol, baud, and bit rates are often confused. Beware.

Semi-Clocked Encodings

• Manchester adds a clock tick to every bit, which uses bandwidth.
• Reduce bandwidth by adding a tick (transition) to only 1 (or 0) bits.
  • 0 (or 1) bits have no tick (transition).

  

• Non-return to zero inverted (NRZI).

Keeping Time

• Long runs of 0s (or 1s) produce troublesome NRZI signals.
  • Long stretches without transitions allow clock drift.

  

• How can long runs of 0s be avoided?

Bit Stuffing

• Prevent long 0 runs by adding a 1 (an NRZI transition) after every n 0s.

  

  • Clocks resync on transitions.
  • N depends on encoding and medium.
• Adding bits to break up runs is called bit stuffing.

Channel Coding

• Bit stuffing is an example of channel coding.
  • Modifying the data stream to provide better transmission characteristics.

  

Line Balance

• For efficient operation, signals should maintain 0-volt short-term averages.

  

• Non-zero averages mean direct-current (DC) signals.
• DC is expensive and difficult to handle.

Balanced Encoding

Use three symbols to encode two bits. Successive 1s (or 0s) alternate in polarity.

Balanced Encoding

This encoding is known as bipolar NRZ Also known as Alternate Mark Inversion (AMI).

• Bipolar because some symbols have opposite polarity.
• Bipolar NRZ is semi-clocking; long runs of zeros cause problems.
  • Bit stuffing can help.

Block Coding

• Other forms of channel coding can also deal with balance and synchronization.
• A n-bit codeword can be mapped into an m-bit block, m < n.
  • Hence the name block coding.
• Artful codeword mappings produce bit sequences with good synchronization and balance.
• These are known as mB/nB block codes.

Example

• This is a 3B/4B block encoding.

  Codeword		Bit Block		Codeword		Bit Block
  0000 0001 0010 0011 0100 0101 0110 0111		— — — — — 000 001 100		1000 1001 1010 1011 1100 1101 1110 1111		— — 010 011 — 101 110 111

• The unused codewords can be mapped as control or status values.

Baseband Transmission

• A wire has maximum bandwidth B Hz.
• Digital transmission hogs all bandwidth for a single bit stream.
  • Parameters set so the line encoder generates maximum frequency B Hz.
  • Any other frequency up to B Hz could be generated too.
• Potentially using all frequencies for a single bit stream is called baseband transmission.

Baseband Problems

• Baseband works well in modest circumstances.
  • Undemanding data loads over short distances.
• Baseband has problems in other circumstances.
  • Some media don’t work well or at all at some frequencies.
  • Giving one bit stream everything creates high latency and delay in other bit streams.

Summary

• A digital signal is an analog encoding of finite levels.
• Line encodings have many knobs to cover many cases.
  • Transitions, polarities, symbols; clocking, balance, efficiency.
• Channel encodings massage the data improve encoding and transmission characteristics.
• Baseband transmission is a private vice; multiplexing is a public virtue.

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This page last modified on 2013 February 25.