Coding technology Lecturer: Prof. Dr. János LEVENDOVSZKY ([email protected]) Course website:...
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Transcript of Coding technology Lecturer: Prof. Dr. János LEVENDOVSZKY ([email protected]) Course website:...
![Page 1: Coding technology Lecturer: Prof. Dr. János LEVENDOVSZKY (levendov@hit.bme.hu) Course website: siposr/kodtech.](https://reader033.fdocuments.in/reader033/viewer/2022051401/5697bfd41a28abf838cacbdb/html5/thumbnails/1.jpg)
Coding technologyCoding technology
Lecturer:
• Prof. Dr. János LEVENDOVSZKY ([email protected])
• Course website: www.hit.bme.hu/~siposr/kodtech
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Course informationCourse information
REQUIREMENTS:•One major tests (and a correction possibility)•Signature is secured if and only if the grade of the test (or its recap) are higher (or equal) than 2 !•The test is partly problem solving !
LECTURES:
•Wednesday 12.15 (MS Lab)
•Thursday 14.15 (MS Lab)
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Suggested literature and referencesSuggested literature and references• T.M. Cover, A.J. Thomas: Elements of Information
Theory, John Wiley, 1991. (IT)
• S. Verdu, S. Mclaughlin: Information Theory: 50 years of discovery, IEEE, 1999 (IT)
• D. Costello: Error control codes, Wiley, 2005
• S. Golomb: Basic Concepts in Information Theory and Coding, Kluwer, 1994. (IT + CT)
• E. Berlekamp: Algebraic Coding Theory. McGraw Hill, 1968. (CT)
• R.E. Blahut: Theory and Practice of Error Correcting Codes. Addison Wesley, 1987. (CT)
• J.G. Proakis: Digital communications,McGraw Hill, 1996
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Basic principle
CHANNEL
noise distortion e-dropping
Limited resources (transmission power, bandwidth …etc.)
Challenge: How can we communicate reliably over an unreliable channel by using limited resoures ? CODING TECHNOLOGY
CHANNELCoding Decoding
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23.04.21. 5
Course objective: algorithmic skills and knowledge (coding procedures) for increasing the performance of
communication systems!
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23.04.21. 6
Constraints & limitations:- Limited power- Limited frequency bands - Limited Interference
Requirements:- high data speed- QoS communication (low BER and low delay)- Mobility
???
Resources (bandwidth, power …etc.) are not available !
Solution: develop intelligent algorithms to overcome these limitations !!!
Why to enhance the performance of wireless communication systems ?
E.g. - low BER requires increased transmission power
- higher data rate requires more radio spectrum
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General objective
Replacing resources by algorithms !!!
Scarce and expensive Cheap and the evolution of underlying computational technology is fast
1800/1350, 1600/1200, and 1336/1000 MIPS/MFLOPS
Multibillion dollar investment
$ 100 investment
Modern communication technologies = smart algorithms and protocols to overcome the
limits of the resources
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23.04.21. TÁMOP – 4.1.2-08/2/A/KMR-2009-0006 8
Frequency allocation
http://en.wikipedia.org/wiki/File:United_States_Frequency_Allocations_Chart_2003_-_The_Radio_Spectrum.jpg
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Main parameters of current wireless systems
TÁMOP – 4.1.2-08/2/A/KMR-2009-0006 923.04.21.
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Demand vs. Capacity and Spectrum Occupancy
1023.04.21. TÁMOP – 4.1.2-08/2/A/KMR-2009-0006
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RESOURCES:RESOURCES: e.g. bandwidth, transmission power
DEMANDS (QoS): DEMANDS (QoS): given Bit Error Rate, Data Speed
QoS = f (resources)
???
The question telecom
companies invest money into
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Spectral efficiency – a fundamental measure of performance
SE [bit/sec/Hz] = what is the data transmission rate achievable over 1 Hz physical sepctrum
present GSM technology SE ~ 0.52 bit/sec/Hz
Information theory: what are the theoretical limits of SE ? (channel dependent 5 Bit/sec/Hz)
Coding theory: by what algorithms can one achieve these theoretical limits ?
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Theoretical endeavours inspired by technology and algorithmic solutions
• Source coding: how far the binary representation of information provided by data sources can be compressed
• Channel coding: how to achieve reliable communication over unreliable channels
• Data security: how to implement secure communication over public (multi-user) channels
• Data compression standards: APC for voice, JPEG, MPEG
Error correcting coding:
MAC protocols (RS codes, BCH codes, convolutional codes)
• Data security: Public key standards (e.g. RSA algorithm)
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Source coding
00000001001000110100
0101
1111
0000 0001 0010 0011 0100 0101 …………0000 0000 1 1 1 1 1 …………0
# of bits appr. One-fourth
symbols codewords
a1 01
a2 10111
a3 111
a4 110
aN 01110
Optimal codetable ?
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Channel coding
Unreliable channel
010010110 0110111010
Unreliable channel
000005x
repeat0
0Majority detector
01010
What is the optimal code guaranteeing a predefined relaibility with minimum loss
of dataspeed?
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Cryptography
Public channelCypher Decyphermessage message
key keyattacker
How can one construct small algorithmic complexity cryptography algorithms which present high algorithmic
complexity for the attacker, in order to yield a given level of data security ?
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SummarySummary
Primer info (voice, image..etc.)
Channel
Retrieved info
Alg.
Corrupt recepetion
QoS: BER, data rate
Challenges:Challenges:
1. What is the ultimately compressed representation of information ?
2. What is the data rate and by what algorithms over which can communicate reliably over unreliable channels ?
3. How can we communicate securely over public systems?
Alg.
Trans. power., bandwidth
RESPURCES
Corresponding algorithms:
Coding technology
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THANK YOU FOR YOR ATTENTION !