CPSC 3600 - DAY 12
FEBRUARY 22, 2017

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FDM Variations

	Spread Spectrum
		Method to combat interference
		Splits the channel into 1/K carriers.
		Transmit all of the data over each of the carriers.
		Use the copy that arrives with the fewest amount of errors
		Intended for use in scenarios where interference is expected.

Hierarchial FDM

	It is possible for multiplexors to group multiple signals into one
	using a hierarchy of frequencies.
	
Wavelenght Division Multiplexing

	Refers to the application of frequency division multiplexing to 
	optical fiber
	Multiplexing, demultiplexing with light.

Time Division Multiplexing (TDM)

	Doesn't rely on electromagnetic energy as FDM does.
	Simply transmits an item from one source to another over time.

Synchronous TDM

	Synchronous Time Division Multiplexing is a type of TDM in which data
	is transmitted continuously with no breaks between data items.

	Senders in STDM use a round-robin ordering to send items, with each
	sender taking turns sending some information.  An item from sender
	one is processed, then from sender two, etc.

TDM for Telephone Systems

	Phones use synchronous TDM

	Demultiplexor can't tell where a data stream slot ends and begins

	To prevent this, an alternating framing bit is added to the start of
	the data stream in each round.

	The demultiplexor looks for alternating framing bit to tell if it is
	synchronized or not.  The data can be retransmitted if there is an 
	error.

Hierarchial TDM

	Like FDM, TDM can be arranged in an hierarchy.

	Instead of using N times the frequency, each successive stage uses N
	times the bit rate, thus the bit rate of each layer is roughly equal
	to the aggregate bit rates of it's inputs (slightly higher due to the
	addition of extra framing bits)

Problems with Synchronous TDM: Unfilled Slot

	STDM works very well if each sender produces data at a uniform, fixed
	rate (1/N of the capacity of the shared medium)

	However, not all sources produce data at a constant rate; many have
	idle time where they are not generating data, which does not work well
	with STDM

	If the sender does not have data to send when it is their turn in the 
	round-robin order, a sequence of "nothing" (like a value of 0 with an
	extra bit set to indicate invalidity) must be sent.

Statistical TDM

	The issue:
		Receivers can usualy be identified by the slot it is sent in.
		But the slots are arbitrary in statistical TDM

	The solution
		Extra overhead
		Each slot gets a receiver identifier.

Code Division Multiplexing

	Each sender is assigned a unique binary code C_i called a chip sequence
	which are orthogonal vectors.

	As well, each sender has a value to transmit, V_i
	
	The senders multiply C_i x V_i and transmit the result

	The senders transmit at the same time and add the result

	To get the value of V_i, you have to multiply the sum by C_i

	(Similar to CDMA in Cell Phones)
	
	+--------------------+-----------------------------+-----------------+
	| Sender	     |	Chip Sequence		   | Data Value	     |
	+--------------------+-----------------------------+-----------------+
	| A		     |	1 0			   | 1010	     |
	+--------------------+-----------------------------+-----------------+
	| B		     |	1 1			   | 0110	     |
	+--------------------+-----------------------------+-----------------+

	First, convert the binary values to vectors, with 0 represented as -1

	C_1 = (1, -1), V_1 = (1, -1, 1, -1)
	C_2 = (1, 1), V_2 = (-1, 1, 1, -1)

	Multiply C1xV1 and C2xV2

	((1, -1), (-1, 1), (1, -1), (-1, 1))
	((-1, -1), (1, 1), (1, 1), (-1, -1))

	The receiver then treats the sequence as a vector, finding the product
	of the vector and chip sequence, treats that result as a sequence, 
	then converts to binary by treating all positive numbers as 1's and
	negative numbers as 0's