1. Multiplexing and Demultiplexing

2. Multiplexing and Demultiplexing
Multiplexing: A network word for sharing
Combining information streams from multiple sources for transmission over a shared medium
Multiplexor: a method/device to implement this.
Demultiplexing: Separating a combined stream back into individual streams

3. Question
Why cannot Verizon users get an iPhone from AT&T and get it work in Verizon's network?

4. The Basic Types of Multiplexing
Four basic approaches
Frequency Division Multiplexing (FDM)
Combination in the frequency domain
Wavelength Division Multiplexing (WDM)
A form of FDM used for optical fiber
Time Division Multiplexing (TDM)
Combination in the temporal domain
Code Division Multiplexing (CDM)
Combination with pure math magic

5. Frequency Division Multiplexing
FMD: Each pair of sender and receiver use a particular carrier frequency.

6. Example: FM broadcasting
101 channels between 87.8 MHz – MHz in North America
NYC:
SC:
Each channel is assigned a frequency band
200KHz
Each channel has a center frequency
Majic 99: 99.5 MHz

7. Frequency Division Multiplexing
Advantage: A dedicated frequency channel for each pair.
Limitation: Frequency interference
Requiring adequate spacing between channels.
Guard band
Number of channels is limited

8. Time Division Multiplexing (TDM)
A simple trick: an item from one source per unit time slot

9. Synchronous TDM
Select sources in a round-robin fashion

10. Unfilled Slots in Synchronous TDM
Many sources generate data in bursts, with arbitrary idle time between them.

11. Statistical TDM Also called asynchronous TDM by some Extra overhead
Select sources in a round-robin fashion
Skip any source that does not have data ready
Extra overhead
ID of the receiver in each slot  MAC address (Ch. 13)

12. Code Division Multiplexing (CDM)
Unlike FDM/TDM, CDM does not rely on any physical property of signals.
Uses an interesting mathematical idea

13. Orthogonal Vector Spaces
(x,y), (x,y,z), (a1, a2, …, an)
Dot product of two vectors a = (a1, a2, …, an) and b = (b1, b2, …, bn)
Must have the same number of elements.
Multiplying the corresponding pairs and adding up the products
Two vectors are said to be orthogonal if their dot product is zero
a∙b = 0
a∙b= a1 b1 + a2 b2 + … + an bn

14. Exercise: Orthogonal or Not?
(1,-1) and (1,1)
(1,1,1,1) and (1, -1, -1, -1)
(0, 0) and (1, 1)
(-2, -1, 1) and (1, 1, 3)
a∙b = 0
Yes, no, yes, yes

15. Example: Two Vector CDM
A sender is assigned a vector, chip sequence, that is orthogonal to all other senders’ chip sequences.
Information from this sender (digitized voice) is processed with this vector.

16. Code Division Multiplexing
The first step consists of converting the binary values into vectors that use -1 to represent 0:
Multiplying C1 x V1 and C2 x V2
The final signal to be sent will be the sum of the two signals

17. Exercise
Compute the final signal that will be transmitted for the following data values:
Sender
Chip Sequence
Data Value A
(1, 0) B
(1, 1)

18. Code Division Multiplexing
On the receiving side
Use the sender A’s vector (1, -1) – chip sequence
Treat the sequence as vectors
Compute the dot product of the vector and the chip sequence
Interpreting the result as a sequence produces: ( )
In binary: ( )

19. Can Other Senders Extract Information?
Suppose Sender B does not send anything.
One receiver uses B’s chip sequence to extract information.
(1, 1) ∙ ( (1, -1), (-1, 1), (1, -1), (-1, 1) )  ( 0, 0, 0, 0)
Implication: A’s information cannot be intercepted by others.

20. Back to the Previous Questions
vs. GSM vs. CDMA
Using very different multiplexing/demultiplexing techniques
GSM: TDM (early version), TDM + FDM
CDMA: Code Division Multiplexing
GSM phones in different countries
May using different frequency bands.
Quad-band: 850, 900, 1800, 1900 MHz
Phones must be able to pick up a right frequency band.
So why no more versatile phones?
Natural technology monopoly/barrier
Consumers are locked into a particular system.