coding technology lecturer: prof. dr. jános levendovszky ([email protected]) course website:...
TRANSCRIPT
Coding technologyCoding technology
Lecturer:
• Prof. Dr. János LEVENDOVSZKY ([email protected])
• Course website: www.hit.bme.hu/~siposr/kodtech
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)
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
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
23.04.21. 5
Course objective: algorithmic skills and knowledge (coding procedures) for increasing the performance of
communication systems!
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
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
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
Main parameters of current wireless systems
TÁMOP – 4.1.2-08/2/A/KMR-2009-0006 923.04.21.
Demand vs. Capacity and Spectrum Occupancy
1023.04.21. TÁMOP – 4.1.2-08/2/A/KMR-2009-0006
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
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 ?
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)
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 ?
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?
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 ?
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
THANK YOU FOR YOR ATTENTION !