Multiplexing and Demultiplexing

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

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

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

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

Example: FM broadcasting 101 channels between 87.8 MHz – 108.0 MHz in North America NYC: http://www.nyradioguide.com/freqlist.htm SC: http://www.statecollege.com/music/radio.php Each channel is assigned a frequency band 200KHz Each channel has a center frequency Majic 99: 99.5 MHz

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

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

Synchronous TDM Select sources in a round-robin fashion

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

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)

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

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

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

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.

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

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

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: (2 -2 2 -2) In binary: (1 0 1 0)

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.

Back to the Previous Questions iPhone@AT&T vs. iPhone@Verizon: 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.