CPS 365
Theophilus Benson
Today’s Lecture
• Recap last class
• Error detection code
– Parity
– Check-Sum
– Error-Correcting-Codes
•
Error correcting code
– Sophisticated code that can correct errors
•
Multiple Access Link
– Ethernet
– Token ring
– Note: understand the concepts
Last Class
• Approaches to Framing
• Latency Breakdown
• Reliable Delivery
– Stop and Wait V. At-Most-Once
• Ensuring high throughput
– Sliding Window
– Seq # V SWS
At Most Once
Goal: send two packets from SW1 to SW3
Assumptions: No Packet Loss
Algorithm: At-Most-Once
SW1
SW2
SW3
At Most Once
SW1
SW2
SW3
Sliding Window
Goal: send two packets from SW1 to SW3
Assumptions: No Packet Loss
Algorithm: Sliding Window
Bandwidth-Delay Product: 4 packet
SWS=4
RWS=4
LFS
SWS
1 2 3 4 5 6
LAR
SW1
SW2
SW3
Sliding Window
SW1
SW2
SW3
At Most Once
Sliding Window
Today’s Lecture
• Recap last class
• Error detection code
– Parity
– Check-Sum
– Error-Correcting-Codes
•
Error correcting code
– Sophisticated code that can correct errors
•
Multiple Access Link
–
–
–
–
Ethernet
Token ring
802.11 (WiFi)
Note: understand the concepts
Why Should You Care About Errors?
• Still happens in:
– Wireless networks
– Cellular networks
• Error detection + Correction is fundamental
– Used to in Storage/Operating Systems
• Crucial in data centers
– Facebook uses advanced forms to protect data
Error Detection
• Must add bits to catch errors in packet
• Sometimes can also correct errors
– If enough redundancy
– Might have to retransmit
• Used in multiple layers
• Three examples today:
– Parity
– Internet Checksum
– CRC
Errors Abound
1 0
SW1
SW2
Errors Abound
• Can we detect the error?
1 1
SW1
SW2
Simplest Schemes:
Repeat Frame N times (FEC)
1 0 1 0 1 0
SW1
SW2
Simplest Schemes:
Repeat Frame N times (FEC)
• Can we detect the error?
• Can we correct errors?
• What is the problem?
1 1 1 0 1 0
SW1
SW2
Simplest Schemes:
Parity Bit
• Add a parity bit to the end of a word
1 0 1
SW1
SW2
Simplest Schemes: Parity Bit
1 Error
• Add a parity bit to the end of a word
• Can we detect the error?
1 1
• Can we correct the error?
1 0
Parity
0
1
0 1
1
0 0
0
0 0 1
SW1
SW2
Simplest Schemes: Parity Bit
2 Errors
• Add a parity bit to the end of a word
• Can we detect error when
1 1
there are two errors?
Parity
0
1 0
1
0 1
1
0 0
0
0 1 1
SW1
SW2
Simplest Schemes: Parity Bit
2 Errors
• Add a parity bit to the end of a word
• Can we detect error when
1 1
there are two errors?
Parity
0
1 0
1
0 1
1
If using this parity, you can only
0 0
0
detect an ‘odd’ number of errors!!!!
0 1 1
SW1
SW2
XoR encoding
1 1 1 0 1 0
SW1
SW2
XoR encoding
1 1 1
XOR
0 1 0
1 0 1
1 1 1 0 1 0 1 0 1
SW1
SW2
XoR encoding
• What happens when there’s an error…
– In the Correcting Code
Error in correcting code
no one cares
1 1 1 0 1 0 0 0 1
SW1
SW2
XoR encoding
• What happens when there’s an error…
– In the Correcting Code
– How about in the data?
Error in Data!!!
Code RED!!!
1 0 0 0 1 0 1 0 1
SW1
SW2
XoR encoding
• What happens when there’s an error…
– In the Correcting Code
– How about in the data?
• How do we correct this?
0 1 0
XOR
1 0 1
1 1 1
1 0 0 0 1 0 1 0 1
SW1
SW2
2-D Parity
• Add 1 parity bit for each 7 bits
• Add 1 parity bit for each bit position across the
frame)
– Can correct single-bit errors
– Can detect 2- and 3-bit errors, most 4-bit errors
• Find a 4-bit error that can’t be corrected
Internet checksum algorithm:
IP Checksum
• Fixed-length code
– n-bit code should capture all but 2-n fraction of errors
• Why?
– Trick is to make sure that includes all common errors
• IP Checksum is an example: 16-bits
– 1’s complement of 1’s complement sum of every 2
bytes
uint16 cksum(uint16 *buf, int count) {
uint32 sum = 0;
while (count--)
if ((sum += *buf++) & 0xffff0000) // carry
sum = (sum & 0xffff) + 1;
return ~(sum & 0xffff);
}
1’s complement
• -x is each bit of x inverted
• If there is a carry bit, add 1 to the sum
• Example: 4-bit integer
– -3: 1100 (invert of 0011)
– -4: 1011 (invert of 0100)
– -3 + -4 = 0111 + 1 = 1000 (invert of 0111 (-7))
How good is it?
• 16 bits not very long: misses how many
errors?
– 1 in 216, or 1 in 64K errors
• Checksum detects all 1-bit errors
• But not all 2-bit errors
– E.g., increment word ending in 0, decrement one
ending in 1
• Checksum also optional in UDP
– All 0s means no checksums calculated
– If checksum word gets wiped to 0 as part of error,
bad news
From rfc791 (IP)
“This is a simple to compute checksum and
experimental evidence indicates it is adequate,
but it is provisional and may be replaced by a
CRC procedure, depending on further
experience.”
Cyclic Redundancy Check
• A branch of finite fields
• Goal: maximize protection, minimize bits
• High-level idea:
– Represent an n+1-bit message with an n degree polynomial
M(x)
– Each bit is one coefficient
– E.g., message 10101001 -> m(x) = x7 + x5+ x3 + 1
– E.g., 11111111-> m(x) = x8+x7 +x6+ x5+x4 +x3+x2+x1 + 1
CRC
• Checking CRC is easy
– Reduce message by C(x), make sure remainder is 0
An example
Original Msg
M(x)
C(x)
Add k 0’s
N(x)
• 8-bit msg: 10011010
• Divisor (3bit CRC):101
• Calculating Checksum
– Select a divisor polynomial C(x),
degree k
– Let n(x) = m(x)xk (add k 0’s to m)
– Compute r(x) = n(x) mod C(x)
– New P(x) = n(x) – r(x)
n(x)
• Checking the Checksum
K-bit CRC
– P(x) mod C(x) = 0
Why is this good?
• Suppose you send m(x), recipient gets m’(x)
– E(x) = m’(x) – m(x) (all the incorrect bits)
– If CRC passes, C(x) divides m’(x)
– Therefore, C(x) must divide E(x)
• Choose C(x) that doesn’t divide any common errors!
–
–
–
–
All single-bit errors caught if xk, x0 coefficients in C(x) are 1
All 2-bit errors caught if at least 3 terms in C(x)
Any odd number of errors if last two terms (x + 1)
Any error burst less than length k caught
Common CRC Polynomials
• Polynomials not trivial to find
– Some studies used (almost) exhaustive search
• CRC-8: x8 + x2 + x1 + 1
• CRC-16: x16 + x15 + x2 + 1
• CRC-32: x32 + x26 + x23 + x22 + x16 + x12 + x11 +
x10 + x8 + x7 + x5 + x4 + x2 + x1 + 1
• CRC easily computable in hardware
Why is this good?
• Easy to Implement in Hardware
– All routers must implement this
• Calculating Checksum
– Select a divisor polynomial C(x),
degree k
– Let n(x) = m(x)xk (add k 0’s to m)
– K-bit shift registers
– Compute r(x) = n(x) mod C(x)
– Mod is XOR
– New m(x) = n(x) – r(x)
– Subtraction is also XOR
An alternative for reliability
• Erasure coding
– Assume you can detect errors
– Code is designed to tolerate entire missing frames
• Collisions, noise, drops because of bit errors
– Forward error correction
• Examples: Reed-Solomon codes, LT Codes, Raptor
Codes
• Property:
– From K source frames, produce B > K encoded frames
– Receiver can reconstruct source with any K’ frames,
with K’ slightly larger than K
– Some codes can make B as large as needed, on the fly
Trade-Off: Efficiency Versus Reliability
No Codes
IP-Checkum
Parity
2d-Parity
XOR
FEC
Today’s Lecture
• Recap last class
• Error detection code
– Parity
– Check-Sum
– Error-Correcting-Codes
•
Error correcting code
– Sophisticated code that can correct errors
•
Multiple Access Link
–
–
–
–
Ethernet
Token ring
802.11 (WiFi)
Note: understand the concepts
Media Access Control
• Control access to shared physical medium
– E.g., who can talk when?
– If everyone talks at once, no one hears anything
– Job of the Link Layer
• Two conflicting goals
– Maximize utilization when one node sending
– Approach 1/N allocation when N nodes sending
Different Approaches
• Partitioned Access
– Time Division Multiple Access (TDMA)
– Frequency Division Multiple Access (FDMA)
– Code Division Multiple Access (CDMA)
• Random Access
– ALOHA/ Slotted ALOHA
– Carrier Sense Multiple Access / Collision Detection
(CSMA/CD)
– Carrier Sense Multiple Access / Collision Avoidance
(CSMA/CA)
– RTS/CTS (Request to Send/Clear to Send)
– Token-based
Case Study: Ethernet (802.3)
• Dominant wired LAN technology
– 10BASE2, 10BASE5 (Vampire Taps)
– 10BASET, 100BASE-TX, 1000BASE-T, 10GBASET,…
• Both Physical and Link Layer specification
• CSMA/CD
– Carrier Sense / Multiple Access / Collision
Detection
• Frame Format (Manchester Encoding):
Ethernet Addressing
• Globally unique, 48-bit unicast address per
adapter
– Example: 00:1c:43:00:3d:09 (Samsung adapter)
– 24 msb: organization
– http://standards.ieee.org/develop/regauth/oui/ou
i.txt
• Broadcast address: all 1s
• Multicast address: first bit 1
• Adapter can work in promiscuous mode
Ethernet MAC: CSMA/CD
• Problem: shared medium
– 10Mbps: 2500m, with 4 repeaters at 500m
• Transmit algorithm
– If line is idle, transmit immediately
– Upper bound message size of 1500 bytes
– Must wait 9.6μs (96-bit time) between back to back
frames
• (Old limit) To give time to switch from tx to rx mode
– If line is busy: wait until idle and transmit immediately
Handling Collisions
• Collision detection (10Base2 Ethernet)
– Uses Manchester encoding. Why does that help?
– Constant average voltage unless multiple
transmitters
• If collision
– Jam for 32 bits, then stop transmitting frame
• Collision detection constrains protocol
– Imposes min. packet size (64 bytes or 512 bits)
– Imposes maximum network diameter (2500m)
– Must ensure transmission time ≥ 2x propagation
delay (why?)
Collision Detection
Me
Check to see
If any one is tx
you
Check to see
If any one is tx
Detects collision
Doesn’t detect
collisions
Collision Detection
Me
Check to see
If any one is tx
you
Check to see
If any one is tx
Detects collision
detect
collisions
When to transmit again?
• Delay and try again: exponential backoff
• nth time: k × 51.2μs, for k = U{0..2min(n,10)-1}
– 1st time: 0 or 51.2μs
– 2nd time: 0, 51.2, 102.4, or 153.6μs
• Give up after several times (usually 16)
Capture Effect
• Exponential backoff leads to self-adaptive
use of channel
• A and B are trying to transmit, and collide
• Both will back off either 0 or 51.2μs
• Say A wins.
• Next time, collide again.
– A will wait between 0 or 1 slots
– B will wait between 0, 1, 2, or 3 slots
• …
Ethernet experience
• 30% utilization is heavy
• Most Ethernets are not light loaded
• Very successful
– Easy to maintain
– Price: does not require a switch which used to be
expensive
Wireless links
 Most common
 Asymmetric: base station and client
node
 Point-to-multipoint
 Radio waves can be received simultaneously
by many devices
Wireless access control
• Can’t use Ethernet protocol
– A node on an Ethernet receives every other node’s
transmissions
– A node on an 802.11 network may be too far from
certain other nodes to receive their transmissions
(and vice versa)
– Problems: hiddlen terminal & exposed terminal
Wireless access control
– Hidden terminal
• A and C can’t hear each other’s collision at B
– Exposed terminal
• B can send to A; C can send to D
• C’s transmission to D will not interfere with A’s ability
to receive from B
802.11 (WiFi) Multiple access with
collision avoidance
• Sender and receiver exchange control frames
– Sender  receiver: Request to send (RTS)
• Specifies the length of frame
– Receiver  sender: Clear to send (CTS)
• Echoes length of frame
– Sender  receiver: frame
– Receiver  sender: ack
– Other nodes can send after hearing ACK
• Node sees CTS
– Too close to receiver, can’t transmit
– Addressing hidden terminals
• Node only sees RTS
– Okay to transmit
– Addressing exposed terminals
MACA – Multiple Access Collision
Avoidance
• Use of additional control frames
– Sender asks receiver whether it is able to receive a
transmission - Request to Send (RTS)
– Receiver agrees, sends out a Clear to Send (CTS)
– Sender sends, receiver Acknowledgements (ACKs)
A
B
RTS
1
3
2
CTS
B
A
C
DATA
4
ACK
C
Detect
Collision
time
Find Transmission
Complete
MACA – continued
• When a node hears an RTS from a
neighboring node, but not the
corresponding CTS, that node can
deduce that it is an exposed terminal
and is permitted to transmit to other
neighboring nodes.
A
B 1
Exposed
Terminal
2
B
A
C
D
CTS
DATA
RTS
C
5
RTS
4
3
D
t1
t2
t3
CTS
t4
6
t5
DATA
t6
time
How to resolve collision
• Two or more nodes detect an idle link and try
to transmit an RTS frame at the same time..
• Sender can’t do collision detection
– Single antenna can’t send and receive at the same
time
• If no CTS after a period of time, then RTS
collide
• Exponential backoff to retransmit
Summary
• Error Detection and Correction
–
–
–
–
FEC
Simple-XOR-FEC (Parity Bit)
XOR-error-correcting codes
IP-Checksum
• Multiple access links
– Ethernet
– 802.11 (WiFi)
– Note: understand the concepts