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ECE 4371, Fall, 2013 Introduction to Telecommunication Engineering/Telecommunication Laboratory. Zhu Han Department of Electrical and Computer Engineering Class 16 Nov. 16 th , 2013. Outline. Project 2, Due 11/25 ARQ FEC Basics. Project 2. Due 11/19/12 - PowerPoint PPT Presentation
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ECE 4371, Fall, 2015
Introduction to Telecommunication Engineering/Telecommunication Laboratory
Zhu Han
Department of Electrical and Computer Engineering
Class 17
Oct. 20th, 2015
OutlineOutline Project 2, Due 12/1
Exam 2, 11/24
Term project
ARQ
FEC Basics
Project 2 Project 2 Due 12/1/14 Take a selfie Show time signal, eye diagram, and constellation for no noise, SNR=0,
SNR=5dB and SNR=10dB. (1 point) Calculate BER for SNR=0. SNR=2.5dB and SNR=5dB, compared with
theoretic result. Change symb to sufficiently large. (2 point) For QPSK and 16QAM, redo the above step (2 point) Transmit images (3 point)
– Test small image first– Alignment for both sampling and data– Calculate PSNR for SNR=0dB, SNR=2.5dB, and SNR=5dB. – Print images
Timing: sampling at the wrong time. 2 point– 1/16, 2/16, … for BER vs. SNR, PSNR vs. SNR
ISIISI
0 2 4 6 8 10 12 14 16-1.5
-1
-0.5
0
0.5
1
1.5
2
Scatter PlotScatter Plot
-1 -0.5 0 0.5 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Qua
drat
ure
In-Phase
Scatter plot
-1.5 -1 -0.5 0 0.5 1 1.5
-1.5
-1
-0.5
0
0.5
1
1.5
Qua
drat
ure
In-Phase
Scatter plot
Eye DiagramEye Diagram
-0.5 0 0.5-1.5
-1
-0.5
0
0.5
1
1.5
Time
Am
plitu
de
Eye Diagram
-0.5 0 0.5-2
-1
0
1
2
Time
Am
plitu
de
Eye Diagram for In-Phase Signal
-0.5 0 0.5-2
-1
0
1
2
Time
Am
plitu
de
Eye Diagram for Quadrature Signal
BER and PSNR vs. SNRBER and PSNR vs. SNR Error Floor for sampling errors
0 1 2 3 4 510
-3
10-2
10-1
100
EbNo (dB)
SE
R a
nd B
ER
Performance of Baseband QPSK
Theoretical SER
Theoretical BERSimulated SER
Simulated BER
SNR
PSNR
ImageImage Original, 5 dB, 2.5 dB, 0 dB, and
Technical WritingTechnical Writing Structure, Logic (between sentences and paragraphs), and Strictness (no holes). Know who is your audiences Structure
– Title and keyword: concise and hit the point, for google users– Abstract: 200 words, for directors who have 20 seconds
Why it is a good topic What is the idea and contribution What are the results
– Introduction: 1 pages, for managers who have 5 minutes Why it is a good topic What are in the literature, or what are the competitors What is the idea and contribution What are the results (Organization)
– System model– Problem formulation, proposed scheme, and analysis– Results– Conclusions– Citations
For peer
Term Project, Choice OneTerm Project, Choice One Due at last regular class so that I can talk about it during
additional class.
Goal: If you have interview on company for wireless project xxx, what you should know
Source– The company listed on the web or some company you know.
– Select the cool project interesting you. Send me an email by 11/10
Structure– Abstract: 100 words for the company, the project and why interests
– Introduction: 1 pages for the company: history, competitors, project lines, future, stocks, etc.
– Main body of 3 pages for a specific product: 2 pages for the thing you have studied from this class, 1 page for something new.
Term Project, Choice twoTerm Project, Choice two What is the state of art of xxx
– Bluetooth, UWB, WLAN, WMAN, 3G, Ad hoc/Sensor Networks
Cognitive Radio, Fiber communication, Cable communication,
Power line communication, Satellite communication, etc.
Source– IEEE communication magazine to get some tutorial papers– Important citations can be found by IEEE Xplore– Citeseer to test if the paper is well cited and recognized– Select a topic by 11/10.
Writing– Goal: suppose you were me and want to give a lecture on the state of art
of xxx.– 200 words abstract, 1 page introduction and 3 pages details, excluding
the figures.– Citations are needed if you “copy” some ideas.
Automatic Repeat-reQuest (ARQ)Automatic Repeat-reQuest (ARQ)
Alice and Bob on their cell phones– Both Alice and Bob are talking
What if Alice couldn’t understand Bob?– Bob asks Alice to repeat what she said
What if Bob hasn’t heard Alice for a while?– Is Alice just being quiet?
– Or, have Bob and Alice lost reception?
– How long should Bob just keep on talking?
– Maybe Alice should periodically say “uh huh”
– … or Bob should ask “Can you hear me now?”
ARQARQ Acknowledgments from receiver
– Positive: “okay” or “ACK”
– Negative: “please repeat that” or “NACK”
Timeout by the sender (“stop and wait”)– Don’t wait indefinitely without receiving some response
– … whether a positive or a negative acknowledgment
Retransmission by the sender– After receiving a “NACK” from the receiver
– After receiving no feedback from the receiver
Error Correcting CodesError Correcting Codes
Adding redundancy to the original message To detect and correct errors Crucial when it’s impossible to resend the message
(interplanetary communications, storage..) and when the channel is very noisy (wireless communication)Information
Source
Message
Transmitter
Noise Source
Destination
Message
Reciever
ReceivedSignal
Signal
Message = [1 1 1 1]
Noise = [0 0 1 0]
Message = [1 1 0 1]
Types of Error Correcting CodesTypes of Error Correcting Codes Repetition Code
Linear Block Code, e.g. Hamming
Cyclic Code, e.g. CRC
BCH and RS Code
Convolutional Code– Tradition, Viterbi Decoding
– Turbo Code
– LDPC Code
Coded Modulation– TCM
– BICM
Repetition CodeRepetition Code
Simple Example: reduce the capacity by 3Simple Example: reduce the capacity by 3
Recovered state
Parity CheckParity Check Add one bit so that xor of all bit is zero
– Send, correction, miss
– Add vertically or horizontally
Applications: ASCII, Serial port transmission
ISDN NumberISDN Number ISBN 10
– a modulus 11 with weights 10 to 2, using X instead of 10 where ten would occur as a check digit
– ISBN 0-306-40615-2
ISBN 13– Calculating an ISBN 13 check digit requires
that each of the first twelve digits of the 13-digit ISBN be multiplied alternately by 1 or 3. Next, take the sum modulo 10 of these products. This result is subtracted from 10.
– ISBN 978-0-306-40615-7.
Hammings SolutionHammings Solution
A type of Linear Block Code
Encoding: H(7,4)
Multiple ChecksumsMessage=[a b c d]
r= (a+b+d) mod 2s= (a+b+c) mod 2t= (b+c+d) mod 2
Code=[r s a t b c d]
Coding rate: 4/7– Smaller, more redundancy, the better protection.
– Difference between detection and correction
Message=[1 0 1 0] r=(1+0+0) mod 2 =1
s=(1+0+1) mod 2 =0
t=(0+1+0) mod 2 =1
Code=[ 1 0 1 1 0 1 0 ]
Error Detection AbilityError Detection Ability
100,000 iterationsAdd Errors to (7,4) dataNo repeat randomsMeasure Error Detection
Error Detection•One Error: 100%•Two Errors: 100% •Three Errors: 83.43%•Four Errors: 79.76%
Stochastic Simulation:
Results:
Fig 1: Error Detection
50%
60%
70%
80%
90%
100%
1 2 3 4Errors Introduced
Per
cen
t E
rro
rs D
etec
ted
(%
)
How it works: 3 dotsHow it works: 3 dots
Only 3 possible words
Distance Increment = 1
One Excluded State (red)
It is really a checksum.
Single Error Detection
No error correction
A B C
A B C
A C
Two valid code words (blue)
This is a graphic representation of the “Hamming Distance”
Hamming DistanceHamming Distance
Definition: – The number of elements that need to be changed (corrupted) to turn one
codeword into another.
The hamming distance from:– [0101] to [0110] is 2 bits
– [1011101] to [1001001] is 2 bits
– “butter” to “ladder” is 4 characters
– “roses” to “toned” is 3 characters
Another DotAnother Dot
The code space is now 4.
The hamming distance is still 1.
Allows:
Error DETECTION for Hamming Distance = 1.
Error CORRECTION for Hamming Distance =1
For Hamming distances greater than 1 an error gives a false correction.
Even More DotsEven More Dots
Allows:Error DETECTION for Hamming Distance = 2.
Error CORRECTION for Hamming Distance =1.
• For Hamming distances greater than 2 an error gives a false correction.
• For Hamming distance of 2 there is an error detected, but it can not be corrected.
Multi-dimensional CodesMulti-dimensional Codes
Code Space:
• 2-dimensional
• 5 element states
Circle packing makes more efficient use of the code-space
Cannon BallsCannon Balls
http://wikisource.org/wiki/Cannonball_stacking
http://mathworld.wolfram.com/SpherePacking.html
Efficient Circle packing is the same as efficient 2-d code spacing
Efficient Sphere packing is the same as efficient 3-d code spacing
Efficient n-dimensional sphere packing is the same as n-code spacing
ExampleExample Visualization of eight code words in a 6-typle space