an example routing illustration
DESCRIPTION
using tracert or traceroute xtraceroute is a graphical version of tracert. an example routing illustration. layer 1: the physical layer. node: router or host host: general purpose computer router: general purpose or custom hardware physical layer connection through network adaptor - PowerPoint PPT PresentationTRANSCRIPT
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 1
an example routing illustration
– using tracert or traceroute– xtraceroute is a graphical version of tracert
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 2
layer 1: the physical layer
• node: router or host
• host: general purpose computer
• router: general purpose or custom hardware
• physical layer connection through network adaptor
• network adaptor: NIC (network interface card)
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 3
topic 1: transmission media
• guided (see next slide)
• unguided– laser, radio satellites
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 4
guided physical media• magnetic media (e.g. tapes & disks)
• twisted pair (e.g. UTP Cat 3, UTP Cat 5)– UTP = Unshielded Twisted Pair; Cat = Category
– (Cat 5 has more twists per cm than Cat 3)
• coaxial cable (e.g. cable TV)– thick
– thin
• optical fiber (e.g. submarine and backbone links)– single mode
– multi mode
• wireless (RF, microwave, infrared)
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 5
coaxial cable (“coax”)
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 6
principles of fiber optics
(a) light rays from inside a silica fiber impinging on the air/silica boundary at different angles
(b) light trapped by total internal reflection
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 7
fiber optic cables
(a) side view of a single fiber
(b) end view of a sheath with three fibers
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 8
two types of fiber optic cables
1. single-mode fiber (SMF): core ~8--12mic
2. multi-mode fiber (MMF): core ~50mic
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 9
intermission
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 10
wired media capacities
cable typical b/w distances
category 5 twisted pair 10 - 100 Mbps 100 mthin-net coax 10 - 100 Mbps 200 mthick-net coax 10 - 100 Mbps 500 mmultimode fiber 100 Mbps 2 kmsingle-mode fiber 100 - 10000 Mbps 40 km
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 11
common carrier bandwidths
service bandwidth
DS1 1.544 MbpsDS3 44.736 MbpsSTS-1 51.840 MbpsSTS-3 155.250 MbpsSTS-12 622.080 MbpsSTS-48 2.488320 GbpsSTS-192 9.953280 Gbps
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 12
signal characteristics & data rates
nature of signal in medium (air/glass/Cu):-
electromagnetic (EM) waves
speed of EM wave depends on medium
example:
speed of light in vacuum: 3 x 108 meters/sec
speed of electrical signals in copper: 2/3 x speed of light in vacuum
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 13
frequency – wavelength relationship
= c' / f
where,
= wavelength of signal
c' = speed of light (EM wave) in given medium
f = frequency of signal
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 14
the electromagnetic spectrum
Radio Infrared UVMicrowave
f(Hz)
FM
Coax
Satellite
TV
AM Terrestrial microwave
Fiber optics
X ray
100
104 105 106 107 108 109 1010 1011 1012 1013 1014 1015 1016
102 106 108 1010 1012 1014 1016 1018 1020 1022 1024104
Gamma ray
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 15
data transmission
q1: what are common problems in signal propagation?
ans: 1. signal attenuation
- and, different frequencies are attenuated differently!
2. delay distortion
- Fourier components travel at different speeds!
3. noise
- thermal noise
- impulse noise
- crosstalk
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 16
data transmission
q2: how do you transmit information (bits)?
ans: by modulation
- superimpose electrical signal (corresponding to bits) onto a carrier wave; then, transmit in the medium
- modulation can be of several types (see next slide)
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 17
information theory
“the sampling theorem” Harry Nyquist, Claude Shannon, et alia
“exact reconstruction of a continuous-time baseband signal from its samples is possible if the signal is bandlimited and the sampling frequency is greater than twice the signal bandwidth
maximum data rate of a finite bandwidth noiseless channel
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 18
data transmission: signaling
DC signaling (i.e., baseband signaling): bits encoded & transmitted as square waves (see next
slide) suitable for short links, low speeds
AC signaling (by modulation of a carrier wave) bits first encoded as square waves (see next slide);
then, use these waves to modulate carrier;
finally, transmit modulated carrier suitable for long-haul links, higher speeds
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 19
modems: electrical representation of data bits
(a) a binary signal
(b) amplitude modulation
(c) frequency modulation
(d) phase modulation
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 20
assertion:
we could use a 2 signal-level system to represent data
i.e., logic 0 = +5v and logic 1 = 0v
any foreseeable problems? yes1. is 0v = logic 0, or is it an idle transmitter?
2. DC bias on line
therefore, we need better encoding strategies
data transmission: bit encoding
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 21
data transmission: bit encoding
four types of encoding schemes:
NRZ (Non-Return to Zero) NRZI (Non-Return to Zero Inverted) Manchester 4B/5B (used in conjunction with NRZI)
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 22
bit encoding (cont'd.): fig 2.10 (textbook)
Bits
NRZ
Clock
Manchester
NRZI
0 0 1 0 1 1 1 1 0 1 0 0 0 0 1 0
required clock rates?
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 23
problems with NRZ?
1. “baseline wander”
- shift in average (source or perceived) signal strength
2. clock recovery problem
- sender-to-receiver synchronization is lost (see next slide)
instead, why not send clock signal over separate wire?
bit encoding
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 24
the clock sync problem(when clock cannot be recovered)
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 25
how to extract bits from received signal
separate clock cable too expensiveso, how to recover clock from data signal?
clock recovery depends on lots of transitions
“string of ones” sync problem (NRZI)
“string of zeros” sync problem (Manchester)
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 26
bit encoding using 4B/5B: table 2.4 (textbook)
4-Bit Data Symbol 5-Bit Code0000 111100001 010010010 101000011 101010100 010100101 010110110 011100111 011111000 100101001 100111010 101101011 101111100 110101101 110111110 111001111 11101
how to encode in 4B/5B ...
1. first encode data into 5-bit code using table shown to right. (5-bit code ensures that no more than 1 leading zero & no more than 2 trailing zeros)
2. then, encode 5-Bit code using NRZI
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 27
does 4B/5B solve clock-sync problem? - long string of zeros? - long string of ones?
what is baud rate? is it the same as bit rate? baud rate of NRZI? baud rate for Manchester encoding? baud rate for 4B/5B?
efficiency of encoding for above schemes? which encoding scheme is most efficient? which one is least efficient?
points to ponder ...
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 28
addendum to topic 1: some additional material on the
physical layer
the material in the following slides is not in your textbook, but has been included here
for your study
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 29
radio transmission
(a) radio waves in the VLF, LF, and MF bands follow curvature of earth
(b) in the HF band, they bounce off the ionosphere
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 30
communication satellites
I. geostationary satellites
II. medium-earth orbit satellites
III. low-earth orbit satellites
IV. satellites versus fiber
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 31
communication satellites
communication satellites and some of their properties
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 32
communication satellite basics
• launched by rockets
• satellites must maintain orbit stationarity
• satellites follow Kepler's laws of planetary motion
• ability to correct orbital drift
• old age of satellite: orbital decay and death
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 33
low-earth orbit satellites -- Iridium
(a) the Iridium satellites form six necklaces around the earth
(b) 1628 moving cells cover the earth
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 34
Globalstar
(a) relaying in space (b) relaying on the ground
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 35
“unguided” laser transmission
convection currents can interfere with laser communication systems
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 36
intermission
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 37
public switched telephone system structure of the telephone system
“POTS”
the politics of telephones “PSTN”, “telco”, “telecom”, “Baby Bells” governments own, operate, and/or regulate
the local loop: modems, ADSL and wireless “last mile”, “first mile”
trunks and multiplexing switching
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 38
structure of the telephone system
(a) fully-interconnected network“complete graph”, “clique”, “mesh” (context sensitive)
(b) centralized switch(c) two-level hierarchy
squares: “mesh” (context sensitive)
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 39
major components of the PSTN
local loops analog twisted pairs going to houses and businesses
trunks digital fiber optics connecting the switching offices
switching offices where calls are moved from one trunk to another
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 40
the local loop: modems, ADSL, and wireless
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 41
wireless local loops
Architecture of an LMDS system.
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 42
DSL: Digital Subscriber Line local loop
Bandwidth versus distance over category 3 UTP for DSL.
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 43
the politics of telephones
LATAs, LECs, and IXCs
Circles are LEC switching offices.
Each hexagon belongs to the IXC whose number is on it.
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 44
FDM: Frequency Division Multiplexing
(a) original bandwidths(b) bandwidths raised in frequency(b) multiplexed channel
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 45
WDM: Wavelength Division Multiplexing
Wavelength division multiplexing.
DWDM, CWDM, ...
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 46
TDM: Time Division Multiplexing
T1 framing
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 47
sampling for transmission over TDM
Delta modulation.
delta modulation
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 48
TDM of multiple data (voice) streams
Multiplexing T1 streams into higher carriers.
U.S. system: Synchronous Optical NETwork (SONET)
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 49
TDM framing
Two back-to-back SONET frames.
two SONET frames in sequence
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 50
standard TDM line rates
SONET and SDH multiplex rates.
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 51
circuit switching vs. packet switching
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 52
circuit, message, and packet switching
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 53
circuit vs. packet switching
previous figures taken from Computer Networks, 4/e, A.S. Tanenbaum
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 54
functions:1. packet framing, bit-stuffing, character stuffing, etc.
2. error detection, error correction
- generate and process acknowledgements
- “checksumming” of packets
3. fragmentation (and reassembly) of packets;
sequence numbering, etc.
4. flow control
5. channel access control (on broadcast/shared media)
the data link layer
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 55
relationship between packets and frames
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 56
why do we frame packets?
because:
1. data packets must be separated from one another
- inserting time gaps between packets does not work
because: network may squeeze out time gaps
2. error checking for individual frames is easy/convenient
1. framing
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 57
the four main ways to frame packets ...
1. using character counts
2. using framing characters, with character stuffing
3. using start and end flags, with bit stuffing
4. clock-based framing (on SONET)
framing methods
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 58
idea:
field in data link header specifies frame size in characters
framing method 1: using character counts
130 .. .. .. .. <checksum>
character count
a frame of 130 characters
• any foreseeable problems?
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 59
problems in using character counts
(a) without errors (b) with one bad error
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 60
idea: special characters (sentinels (delimiters)) tell receiver when frames begin or end:
framing method 2:using framing characters, with character stuffing
STX <Header> A C B E F <Trailer> ETX
STX = start of transmission, ETX = end of transmission
example frame with payload 'ACBEF' provided by network layer:
• any foreseeable problems?
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 61
what if 'STX' or 'ETX' occur accidentally in data?
solution: use stuffing character DLE!
DLE = Data Link Escape (term “escaped character” ring a bell?)
example:
suppose sender's network layer sends following data to its DL layer:
A C B ETX M STX B G
then, sender's DL layer transmits the following over the physical layer:
STX <Hdr> A C B DLE ETX M DLE STX B G <Trlr> ETX
and, receiver's DL layer destuffs & sends following data to its network layer:
STX <Hdr> A C B DLE ETX M DLE STX B G <Trlr> ETX
-what if DLE occurs in payload?
glitch in character stuffing
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 62
what if 'DLE' itself occurs accidentally in data?
solution: then stuff DLE, as shown before!
example:suppose sender's network layer sends following data to its DL layer:
A C DLE M STX Gthen, sender's DL layer transmits the following over the physical layer:
STX <Hdr> A C DLE DLE M DLE STX G <Trlr> ETX
and, receiver's DL layer destuffs & sends following to its network layer:
STX <Hdr> A C DLE DLE M DLE STX G <Trlr> ETX
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 63
any disadvantages of character-based framing?
• DLE, STX, ETX are all ASCII characters
• some hardware explicitly supports ASCII, some does not
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 64
idea: special bit patterns (“sentinels”, “flags”, “delimiters”) tell receiver when frames begin or end:
framing method 3:using framing bits (flags), with bit stuffing
01111110 101110..100010111<Trailer> 01111110<Header>
01111110 = flag indicating Start of Frame01111110 = flag indicating End of Frame
example:
resulting DL frame
but, what if framing flags occur accidentally in data?
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 65
solution: prevent this as follows ... after every five consecutive 1s, automatically stuff a 0!
example:source network layer sends following to DL layer ...
1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1
then, source DLL sends following over PHY layer ...
01111110 1 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 01111110
... sink DLL destuffs & sends following to its network layer:
01111110 1 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 01111110
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 66
what if error(s) occur(s) in transmission?
consider an earlier example:
01111110 1 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 01111110
case 1: error is in any position except framing flags
case 2: error is in framing flag itself
can receiver recover from error(s)?
what about from character stuffing errors in DLE, ETX, STX characters?
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 67
idea: in a SONET frame, the first 2 bytes contain a flag; frames are periodic; but, no bit stuffing! why? ...
framing method 4:clock-based framing (SONET)
Overhead Payload
90 columns
9 rows
STS-1 frame
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 68
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 69
errors in transmission
wave-guided digital transmission
copper
fiber
analog transmission
wireless
single-bit errors
burst errors
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 70
error control
error detection
error correction (FEC)
ACKs, NACKs
timers, timeouts
sequence numbers
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 71
• basic idea: add redundant information1. naïve method
• k redundant bits per n-bit message, for k << n• the k bits: “error detecting code”
2. parity3. 2-dimensional parity4. checksumming5. cyclic redundancy check (CRC)
error detection
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 72
error detection: 2-D parity
1011110 1
1101001 0
0101001 1
1011111 0
0110100 1
0001110 1
1111011 0
Paritybits
Paritybyte
Data
“odd parity” or “even parity”?
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 73
2-D parity
does this catch all errors? ..
how about:
1-bit errors?
2-bit errors?
3-bit errors?
4-bit errors?
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 74
error detection: checksumming
source:1. add up all the data words to find checksum2. transmit checksum along with original data
sink:1. extract checksum from frame2. compute its own checksum on received data3. computed checksum == extracted checksum?4. if comparison fails, then reject frame
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 75
checksumming
advantage: easy, fast, efficientdisadvantage: weak protection (link layer not)
implementation:
• add using 1's complement arithmeticwhy? ... because
1. easy to implement in hardware2. fast in software3. implementation is big-endian/little-endian neutral
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 76
checksumming
one's complement arithmetic
additive inverse == bitwise complement
not(x), x', x-bar
zero: 00...00; -zero: 11...11
one’s complement of x = x’
0 + x = x’; -0 + x = x’
to subtract by x, add x’
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 77
checksumming
use 4-bit numbers in 1's complement for ...
(pay particular attention to carry and overflow rules)
3 + 4
5 + (-2)
5 + (-6)
(-5) + 6
(-3) + (-4)
(-5) + (-6)
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 78
checksumming
IP packet header checksum:
1's-complement of
16b 1's complement sum of
all 16b words in header
check at receiver:
1's complement sum over all 16b words
including checksum word
if result == -0 (FF), then header is valid
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 79
error detection: CRC
how to use CRC?
Data
Data CRC bits
Compute CRC
Add other headers, framing bits; then transmit
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 80
CRC
idea:
1. think of an (n+1) bit message as an 'n' degree polynomial; call this M(x)
e.g., 10011010 = x7+x4+x3+x1
2. select suitable 'divisor' polynomial (aka generator polynomial) of degree k ( k < n)
e.g., G(x) = x3+x2+1
(here, note that k = 3)
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 81
CRC
idea (cont'd.):
3. calculate CRC bits using modulo-2 arithmetic; append these bits at the end of data bits; call all of this T(x):
Data CRC bits
T(x)
goal: make T(x) exactly divisible by G(x) before transmision; receiver then computes T(x) / G(x)
if T(x) is not exactly divisible by G(x), then received frame is bad
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 82
CRC
• how to make T(x) exactly divisible by G(x)?• here's how: N / D = (Q, R)
• therefore, (N-R) / D = (Q, 0)
1. calculate xk * M(x):
Data 0 ... 0
P(x)
M(x)k zeros
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 83
CRC
(how to make T(x) exactly divisible by G(x)? (contd.))
2. compute P(x) / G(x) using modulo-2 division
3. subtract remainder R(x) from P(x)
then, we have:
T(x) = P(x) – R(x) ... see figure below
thus, T(x) is perfectly divisible by G(x)
Data CRC
T(x)
M(x)k bits
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 84
CRC
rules of polynomial arithmetic modulo 2:
• if deg(B(x)) > deg(C(x)), then B(x) is divisible by C(x)
• if deg(B(x)) = deg(C(x)), then B(x) is divisible by C(x) once
• B(x)/C(x) = B(x) – C(x)
• B(x) – C(x) = B(x) XOR C(x)
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 85
CRC
example from text (page 99):
given:
G(x) = x3+x2+1
M(x) = x7+x4+x3+x1
what is the value of P(x)?
(i.e., what bits are actually transmitted by the sender?)
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 86
CRC
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 87
CRC• how could an error escape the CRC method?• let E(x) be the errors “added” to T(x)• so, T(x) + E(x) is the incorrectly transmitted
frame
• one-bit error?• two-bit error?• error with odd number of bits?• burst error?
1500B (12000b) Ethernet frame: 32b CRC
Don Montgomery, CSE Department, Southern Methodist University – ECS 4344 Ch2, slide 88
[needs work] Error Detection and Correction
Hamming distance (h) Error detection d H >= d+1 Hamming code
Burst error detection using hamming code Product codes