Carriers, Modulation, Modems, Packets, Frames, Error Detection

Carriers

each medium has specific frequencies that it carries best
e.g. fiber carries optical-frequency signals, radio carries radio-frequency signals
very few media carry DC signals (very low frequencies) well
we can use a higher-frequency signal and vary it over time to carry a lower-frequency signal
example: turn light on and off to carry bits (amplitude modulation)

AM radios
the frequency of the carrier is constant
the power of the carrier is modified ( modulated) according to the power of the signal we want to carry
a 1-bit might be a full-power signal, a 0-bit a half-power signal, no bit could be no signal

FM radios, TV
the power of the carrier is constant
the frequency of the carrier is modulated according to the power of the signal we want to carry
Frequency-Shift Key (FSK) wireless transmission: frequency f₁ is one bit, frequency f₂ is the other bit

the power and the frequency of the carrier are constant
the phase of the carrier is modulated by the signal
e.g. if we can send 8 different phases, we select the phase based on the next 3 bits, and send (one cycle) using that phase
in this case, the bit rate would be 3 times more than the baud rate (the rate at which signals change)
a modulator encodes the signal on the wire, a demodulator must look at the signal and attempt to decode it

a Modulator/Demodulator pair is called a Modem
modems often use Phase-Shift modulation, encoding several bits per baud
a modem pair needs four wires for communication: two for signal/return from modem A to modem B, and two for signal/return from B to A (the two return wires could be combined, but at the cost of additional noise)
such a set of two twisted pairs is a serial line (a term also applied to RS-232)
serial lines are point-to-point: they can only connect two modems at any given time

wireless modems:
- antennas instead of wires
- very careful to only broadcast in the assigned frequencies (or the FCC will complain very quickly!)
dialup modems:
- able to sense dial tone, ringing voltage
- one side must dial the number ("pushbutton" tones, "dial" clicking)
- the other side must answer
- two-way communication requires handoff or different carriers

different carriers can be used simultaneously without interference -- like tuning to stations on the radio (all radio stations are transmitting at the same time)
broadband transmission allows different bands to be used at the same time to carry different signals
for example, can use different frequencies or colors of light on the same optic fiber, then must split them apart at the receiver, perhaps using a prism
this is Frequency Division Multiplexing, FDM
in Time Division Multiplexing, TDM, we first send a bit (or frame) from one source, then the next, in round-robin fashion.

anything that uses more than one channel is "spread spectrum"
generally, we use more bandwidth to gain better S/N ratio
Direct Sequence Spread Spectrum: a specific combination of channel on/offs (" chips") represents a given bit
Frequency Hopping Spread Spectrum: after sending a bit (frame) in one channel, we send one on another, and so on
to avoid mutual interference, both the chips and the frequency hopping sequence are varied pseudorandomly

assume a slow link is shared among several pairs of computers
if one computer (pair) is transferring a large file over the link, the transfer will take a long time
how could the others use the link at the same time?
use time-domain multiplexing: break each transfer into packets with a given maximum size (e.g. 1024 bytes), and transfer packets from each sender in turn
the big sender sees less effective bandwidth,
but the latency for the others is much better

assume we have a way of sending and receiving bits and bytes
how would we send a packet?
in other words, at the receiver, given a real-time sequence of bytes, how do we know (in real-time) where a packet starts and ends?
answer: use a special character (e.g. 255) to mark the start of the packet, another (e.g. 254) to mark the end

Serial Line IP protocol: carries IP packets on serial lines
two special characters: END and ESCape
END marks the end of a packet (and the start of the next)
data may contain the special characters:
- if the data byte is END, we send ESC END
- if the data byte is ESC, we send ESC ESC
predefined maximum user data size, 1024 bytes
RFC 1055, http://www.ietf.org/rfc/rfc1055.txt

SLIP is an example of byte stuffing:
- reserve one or more characters for marking beginning and end
- if the character occurs in the data, escape it
some protocols use bit stuffing as well. For example, some protocols use 5 ones in a row to mark a special case
- If the data contains 4 ones in a row, a zero is always inserted after those 4 bits
- the receiver always removes a zero following 4 ones
- the receiver can tell the special case when it receives 5 ones in a row

bit errors: errors that have an equal likelihood of being equally distributed among all the bits in a message
burst errors: errors that are more likely to corrupt bits near other errors
if I have a bit error rate b, and there are P bits in a packet, my packet error rate (likelihood of at least one error in a packet) is about 1 - (1 - b)^P
Error pattern: if I send 0101010101 and receive 0101100101, if I XOR the two I get the error pattern, 0000110000
compute the packet error rate when the bit error rate is 10^-9 and each packet carries 125 bytes (no calculators)

one way to detect all single-bit errors is to compute the XOR of all the bits in the message, and send that bit: this is the {\em even parity} bit
a single bit error will change the message so the parity no longer matches
the (boolean) inverse of even parity is odd parity
RS-232 allows the configuration of even, odd, or no parity bit
when parity is configured, an additional parity bit is sent with each character
but double-bit errors (and any error with an even numbers of bits) will not be detected

if we add all the bytes in the message
and send the sum,
the receiver can repeat the operation and detect most errors
unless one error adds, and one subtracts the same amount
Internet checksum:
- add all 16-bit words in the message,
- add any 16-bit carry back in
- invert before sending
- receiver should compute 0xFFFF or 0x0

Cyclic Redundancy Check (Peterson, 1962)
used for networks, storage media
a class of error control codes
mathematically designed to detect all single-bit errors, all double-bit errors, and most multi-bit and burst errors
defined by a polynomial with binary (0 or 1) coefficients
example: x³² + x²⁶ + x²³ + x²² + x¹⁶ + x¹² + x¹¹ + x¹⁰ + x⁸ + x⁷ + x⁵ + x⁴ + x² + x + 1 (Ethernet, ATM)
example: x⁸ + x² + x + 1 (ATM)

the highest exponent of the polynomial is the number of bits in the CRC
the message is (logically) processed one bit at a time
logically, there is a shift register with a bit for every exponent of the polynomial
where the polynomial has a non-zero coefficient, we XOR the MSB of the shift register with the output of the corresponding bit of the shift register before shifting into the next position
the final value in the register is the CRC: it is inverted and sent
the receiver performs the same calculation and gets zero if there was no error