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Introduction to Computer
Networks
CMPE 150
Fall 2005
Lecture 13
CMPE 150- Introduction to Computer Networks
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Announcements
• Midterm postponed!
– Instead of 10.28, it will be on 11.04!
• Lab next week:
– Discussion sessions on protocol pseudo-code
(from Tanenbaum Chapter 3).
– Also, checksum calculation practice!
• Homework 2 due on Monday, 10.24.
CMPE 150- Introduction to Computer Networks
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Hamming Code (Revisited)
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Hamming Code
• Check bits in power-of-two positions.
• Each check bit verifies a set of data bits.
• A data bit is checked by multiple check bits.
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Hamming Code (Cont’d)
• Parity computations:
–
–
–
–
11: 1, 2, 8
10: 2, 8
9: 1, 8
7: 1, 2, 4
- 6: 2, 4
- 5: 1, 4
- 3: 1, 2
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Hamming Code: Example 1
Data: 1001000 using even parity (counting
from right to left).
0
1
11 10 9
0
8
0
7 6
1
0
0
0
5 4
3 2
1
1: 1, 3, 5, 7, 9, 11
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Hamming Code: Example 1
(Cont’d)
Data: 1001101 using even parity (counting
from right to left).
1 0
0
11 10
1
9
8
7
1
0
1
6
5
4
1
3
2
1
1: 1, 3, 5, 7, 9, 11
1
0
0
1
1
1
0
0 1
0
1
11 10 9
8
7
6
5
4
2
1
2: 3, 6, 7, 10, 11
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Hamming Code: Example 2
What if instead of 1 0 0 1 1 1 0 0 10 1, receiver
gets 1 0 0 1 0 1 0 0 1 0 1?
11 10 9 8 7 6 5 4 3 2 1
. Receiver takes frame received and re-computes check bits.
. 1, 3, 5, 7, 9, 11: 1, 1, 0, 0, 1 => 1
. 2, 3, 6, 7, 10, 11: 0, 1, 1, 0, 0, 1 => 1
. 4, 5, 6, 7 : 0, 0, 1, 0 => 1
. 8, 9, 10, 11: 1, 0, 0, 1 => 0
0
1
1
1
Result: Bit in position 0 1 1 1 is wrong!
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How much code redundancy?
• How many check bits needed, i.e., given m
data bits, how many more bits (r) are needed
to allow all single-bit errors to be corrected?
–
–
–
–
Resulting frame is m + r.
(m+r+1) <= 2r.
Given m, then find r.
Example: If m = 7 (ASCII 7 code), minimum r
is 4.
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Hamming Code: Example
7-bit
. Hamming codes can only correct single errors.
. But, to correct bursts of errors, send column by column.
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Flow + Error Control
• Frame revisited.
–
–
–
–
Layer 2 encapsulation/decapsulation.
Flags.
Trailer: checksum.
Header: type, sequence number, ack.
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Stop-and-Wait
• Simplest form of flow control.
• How does it work? (assume error-free
channel)
– (1) Send 1 frame;
– (2) Wait for ACK.
– (3) Go to 1.
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Stop-and-Wait: Pros and Cons
• Very simple!
• But, poor link utilization.
– High data rates.
– Long propagation delay.
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Stop-and-Wait in Noisy Channels
• Need timers, retransmissions, and duplicate
detection.
• Use sequence numbers.
– Why?
– Distinguish frames.
– How large (e.g., in number of bits) are
sequence numbers?
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ARQ Protocols
• Automatic Repeat Request.
– Protocols that wait for ACK before sending
more data.
• ACKs now are used for flow AND error
control.
• What can happen?
– At receiver: frame arrives correctly, frame
arrives damaged, or frame does not arrive.
– At sender: ACK arrives correctly, ACK arrives
damaged, or ACK does not arrive.
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ARQ Protocols
• Sender:
– Send frame 0.
– Start timer.
– If ACK 0, arrives, send
frame 1.
– If timeout, re-send
frame 0.
CMPE 150- Introduction to Computer Networks
• Receiver:
– **Waits for frame.
– If frame arrives, check
if correct sequence
number.
– Then send ACK for
that frame.
– Go to (**)
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Simplex versus Duplex
Transmission
• Simplex:
– Send data in one channel and control in
another channel.
• Duplex:
– Send data and control on the same chanel.
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Can we do better?
• Can we do better?
– Piggybacking.
– Bi-directional transmission.
– Wait for data packet and use that to piggyback
the ACK.
– Use ACK field: only a few additional bits in the
header.
• But, how long should Layer 2 wait to send an
ACK?
– ACK timers!
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Sliding Window Protocols
• Window: number of “outstanding” frames at
any given point in time.
– So what’s the window size of Stop and Wait?
• Every ACK received, window slides.
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Sliding Window: Example
• A sliding window of size 1, with a 3-bit sequence
number.(a) Initially; (b) After the first frame has
been sent; (c) After the first frame has been
received;(d) After the first acknowledgement has
been received.
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Sliding Window: Basics
• Allows multiple frames to be in transit at the
same time.
• Receiver allocates buffer space for n frames.
• Transmitter is allowed to send n (window size)
frames without receiving ACK.
• Frame sequence number: labels frames.
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Sliding Window: Receiver
• Receiver ack’s frame by including sequence
number of next expected frame.
– Cumulative ACK: ack’s multiple frames.
• Example: if receiver receives frames 2,3, and 4,
it sends an ACK with sequence number 5,
which ack’s receipt of 2, 3, and 4.
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More Sliding Window …
• Sender maintains sequence numbers it’s
allowed to send; receiver maintains sequence
number it can receive.
• Sequence numbers are bounded; if frame
reserves k-bit field for sequence numbers,
then they can range from 0 … 2k -1k.
• Transmission window shrinks each time frame
is sent, and grows each time an ACK is
received.
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Example: 3-bit sequence number
and window size 7
A (Sender)
B (Receiver)
0 1 2 3 4 5 6 7 0 1 2 3 4…
0123456701234
0
1
0123456701234
2
ACK 3
0123456701234
0123456701234
0123456701234
0123456701234
ACK 4
0123456701234
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45 0 1 2 3 4 5 6 7 0 1 2 3 4
6
0123456701234
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One-Bit Sliding Window Protocol
Two scenarios: (a) Normal case. (b) Abnormal case.
Notation is (seq, ack, packet number). An * indicates where a
network layer accepts packet. ACK indicates last sequence
number received.
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Bandwidth-Delay Product
• How large should the sender’s window be?
• Function of how “fat” is the pipe?
BW
S
R
RTT
W = BW*RTT/data size
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Pipelining
Receiver’s
window size
is 1: discard
frames after error
with no ACK.
Go Back N
Receiver’s
window size
is large: buffers
all frames until error
Selective Repeat
recovered.
• Pipelining and error recovery. Effect on error when (a)
Receiver’s window size is 1. (b) Receiver’s window size is
large.
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