Ch. 11: Multiplexing and Demultiplexing

Multiplexing
1. Combining multiple streams for transmission over a single channel.
2. Signals must be demultiplexed at the receiver.
3. Target channel is usually a physical connection, but might be virtual, such a s TCP connection.
Types of multiplexing
1. Frequency Division Multiplexing (FDM). Each signal uses its own frequency.
2. Wavelength Division Multiplexing (WDM). This is just FDM when applied to light signals.
3. Time Division Multiplexing (TDM). Taking turns.
4. Code Division Multiplexing (CDM). Magic. Signals are combined and separated using mathmatical operations.
Frequency Division Multiplexing (FDM).
1. Method used for broadcast radio stations or TV channels.
2. Each signal is assigned a range of frequencies called a “channel.”
3. Each signal is then modulated to a carrier frequency in the center of its channel.
4. These are all sent on the same line; the line contains the sum of the signals.
5. The demultiplexor is a collection of filters.
6. A filter is a specialized circuit which attenuates frequecies outside the channel.
7. Channels are separated by a “guard band” to avoid intra-channel interference.
Wave Division Multiplexing (WDM).
1. Same using light.
2. Separated and combined with prisms.
3. Channels frequencies are sometimes called “colors.”
Time Division Multiplexing (TDM)
1. Taking turns.
  1. Synchronous TDM. Each sender is given a turn in rotation.
  2. The data for a channel is broken into peices which are sent in turn.
  3. Synchronization
    1. A known bit pattern is sent between rounds to maintain recevier synchronization.
    2. Telephone systems use alternating 1 and 0.
    3. This stream of bits forms a “framing channel.”
2. Statistical TDM
  1. Sychnronous TDM gives each sender a slot, even when it has nothing to send.
  2. Statistical TDM just skips those.
  3. But needs to add a identifier for each frame, since the recevier can no longer count on strict rotation.
Code Division Multiplexing (CDM)
1. Used in cell phones.
2. Bit sequences are represented as vectors, where sign of each component gives the binary value.
3. Data from senders is combined mathematically, combination is sent, receiver separates them again.
  1. Stations are assigned special identifiers (“chip sequences.”), whose vector representations are orthognal (perpendicular).
  2. Data blocks are combined with their receivers id using the vector cross product.
  3. These cross products are summed, and the resulting bit sequence sent.
  4. The receiver can recover the message by taking the dot product of the received message and its own id.
4. Example from text. Two-bit identifiers.
  1. ID numbers, 10 and 11. Vector forms, (1,−1) and (1,1).
  2. They are orthogonal: (1,−1)⋅(1,1)=1⋅1+−1⋅1=0
  3. Data sent to each address, 1010 and 0110, respectively. Vector forms (1,−1,1,−1) and (−1,1,1,−1)
  4. Compute the cross product of each destination and its message:
    (1,−1)×(1,−1,1,−1)=
    ((1⋅1,−1⋅1),(1⋅−1,−1⋅−1),(1⋅1,−1⋅1),(1⋅−1,−1⋅−1))=
    ((1,−1),(−1,1),(1,−1),(−1,1))
    (1,1)×(−1,1,1,−1)=
    ((1⋅−1,1⋅−1),(1⋅1,1⋅1),(1⋅1,1⋅1),(1⋅−1,1⋅−1))=
    ((−1,−1),(1,1),(1,1),(−1,−1))
  5. Take the sum of these numbers:
    
    1 −1 −1 1 1 −1 −1 1
    
    + −1 −1 1 1 1 1 −1 −1
    
    0 −2 0 2 2 0 −2 0
  6. Author doesn't say how this value transmitted. Presumably a signal with an approriate number of levels.
  7. Each receiver turns it back into a vector and takes the cross product with its id
    (1,−1)⋅((0,−2),(0,2),(2,0),(−2,0))=
    ((1⋅0+−1⋅−2),(1⋅0+−1⋅2),(1⋅2+−1⋅0)(1⋅−2+−1⋅0))=
    (2,−2,2,−2)
  8. Result is interpreted as 1010, the original message. Other receiver will be able to extract its message by the same procedure.
5. Avoids delays caused by TDM in large networks.
Inverse Multiplexing
1. Sometimes, only low-bandwidth channels are available.
2. But, if you afford to use several:

	1	−1	−1	1	1	−1	−1	1
+	−1	−1	1	1	1	1	−1	−1
	0	−2	0	2	2	0	−2	0